Mathematics
Geometry
A cyclic quadrilateral has one interior angle 115°. Find its opposite angle.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 57°
B. 65°
C. 81°
D. 73°
Correct Answer: B
Opposite angles of a cyclic quadrilateral are supplementary: 180°−115°=65°.
Mathematics
Geometry
A cyclic quadrilateral has one interior angle 110°. Find its opposite angle.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 78°
B. 70°
C. 62°
D. 86°
Correct Answer: B
Opposite angles of a cyclic quadrilateral are supplementary: 180°−110°=70°.
Mathematics
Geometry
A cyclic quadrilateral has one interior angle 105°. Find its opposite angle.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 67°
B. 75°
C. 91°
D. 83°
Correct Answer: B
Opposite angles of a cyclic quadrilateral are supplementary: 180°−105°=75°.
Mathematics
Geometry
A cyclic quadrilateral has one interior angle 100°. Find its opposite angle.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 88°
B. 72°
C. 80°
D. 96°
Correct Answer: C
Opposite angles of a cyclic quadrilateral are supplementary: 180°−100°=80°.
Mathematics
Geometry
A cyclic quadrilateral has one interior angle 95°. Find its opposite angle.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 93°
B. 77°
C. 101°
D. 85°
Correct Answer: D
Opposite angles of a cyclic quadrilateral are supplementary: 180°−95°=85°.
Mathematics
Geometry
A cyclic quadrilateral has one interior angle 90°. Find its opposite angle.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 90°
B. 106°
C. 98°
D. 82°
Correct Answer: A
Opposite angles of a cyclic quadrilateral are supplementary: 180°−90°=90°.
Mathematics
Geometry
A cyclic quadrilateral has one interior angle 85°. Find its opposite angle.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 111°
B. 95°
C. 87°
D. 103°
Correct Answer: B
Opposite angles of a cyclic quadrilateral are supplementary: 180°−85°=95°.
Mathematics
Geometry
A cyclic quadrilateral has one interior angle 80°. Find its opposite angle.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 92°
B. 108°
C. 100°
D. 116°
Correct Answer: C
Opposite angles of a cyclic quadrilateral are supplementary: 180°−80°=100°.
Mathematics
Geometry
A cyclic quadrilateral has one interior angle 75°. Find its opposite angle.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 105°
B. 113°
C. 97°
D. 121°
Correct Answer: A
Opposite angles of a cyclic quadrilateral are supplementary: 180°−75°=105°.
Mathematics
Geometry
A cyclic quadrilateral has one interior angle 70°. Find its opposite angle.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="82" y1="52" x2="185" y2="135" stroke="#2563eb" stroke-width="2.5"/><text x="72" y="47" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">A</text><text x="190" y="146" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">B</text></svg>
A. 126°
B. 110°
C. 102°
D. 118°
Correct Answer: B
Opposite angles of a cyclic quadrilateral are supplementary: 180°−70°=110°.
Mathematics
Geometry
Find the area of a semicircle of radius 13 cm. Use π≈3.1416.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=13</text></svg>
A. 265.46 cm²
B. 275.46 cm²
C. 260.46 cm²
D. 270.46 cm²
Correct Answer: A
Semicircle area=½πr²≈265.46 cm².
Mathematics
Geometry
Find the area of a semicircle of radius 12 cm. Use π≈3.1416.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=12</text></svg>
A. 221.19 cm²
B. 226.19 cm²
C. 231.19 cm²
D. 236.19 cm²
Correct Answer: B
Semicircle area=½πr²≈226.19 cm².
Mathematics
Geometry
Find the area of a semicircle of radius 11 cm. Use π≈3.1416.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=11</text></svg>
A. 195.07 cm²
B. 190.07 cm²
C. 185.07 cm²
D. 200.07 cm²
Correct Answer: B
Semicircle area=½πr²≈190.07 cm².
Mathematics
Geometry
Find the area of a semicircle of radius 10 cm. Use π≈3.1416.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=10</text></svg>
A. 152.08 cm²
B. 162.08 cm²
C. 167.08 cm²
D. 157.08 cm²
Correct Answer: D
Semicircle area=½πr²≈157.08 cm².
Mathematics
Geometry
Find the area of a semicircle of radius 9 cm. Use π≈3.1416.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=9</text></svg>
A. 132.23 cm²
B. 137.23 cm²
C. 127.23 cm²
D. 122.23 cm²
Correct Answer: C
Semicircle area=½πr²≈127.23 cm².
Mathematics
Geometry
Find the area of a semicircle of radius 8 cm. Use π≈3.1416.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=8</text></svg>
A. 100.53 cm²
B. 110.53 cm²
C. 95.53 cm²
D. 105.53 cm²
Correct Answer: A
Semicircle area=½πr²≈100.53 cm².
Mathematics
Geometry
Find the area of a semicircle of radius 7 cm. Use π≈3.1416.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=7</text></svg>
A. 86.97 cm²
B. 71.97 cm²
C. 76.97 cm²
D. 81.97 cm²
Correct Answer: C
Semicircle area=½πr²≈76.97 cm².
Mathematics
Geometry
Find the area of a semicircle of radius 6 cm. Use π≈3.1416.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=6</text></svg>
A. 51.55 cm²
B. 56.55 cm²
C. 66.55 cm²
D. 61.55 cm²
Correct Answer: B
Semicircle area=½πr²≈56.55 cm².
Mathematics
Geometry
Find the area of a semicircle of radius 5 cm. Use π≈3.1416.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=5</text></svg>
A. 44.27 cm²
B. 49.27 cm²
C. 39.27 cm²
D. 34.27 cm²
Correct Answer: C
Semicircle area=½πr²≈39.27 cm².
Mathematics
Geometry
Find the area of a semicircle of radius 4 cm. Use π≈3.1416.<br/><svg xmlns="http://www.w3.org/2000/svg" width="260" height="180" viewBox="0 0 260 180" role="img"><circle cx="130" cy="95" r="65" fill="none" stroke="#1f2937" stroke-width="2"/><circle cx="130" cy="95" r="3" fill="#111"/><text x="137" y="91" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">O</text><line x1="130" y1="95" x2="195" y2="95" stroke="#2563eb" stroke-width="2.5"/><text x="153" y="85" style="font-family:Arial,sans-serif;font-size:13px;fill:#111;">r=4</text></svg>
A. 20.13 cm²
B. 25.13 cm²
C. 35.13 cm²
D. 30.13 cm²
Correct Answer: B
Semicircle area=½πr²≈25.13 cm².