Inscribed Angle from Intersected Arc (Level 2)

This math topic focuses on solving problems related to the geometry of circles, specifically calculating inscribed angles from given intersected arcs. The problems require users to find the measure of an angle based on the degrees of the arc opposite the angle. These exercises are designed for students with intermediate knowledge of geometry and provide a practical application of the Inscribed Angle Theorem, which states that the inscribed angle is half the measure of its intercepted arc. The questions include multiple-choice answers, enhancing the problem-solving skills needed to determine and verify the correct inscribed angle values.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Geometry of Circles - Inscribed Angle from Intersected Arc Worksheet

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Geometry of Circles - Inscribed Angle from Intersected Arc
1
An svg image showing a math problem
Find angle DBN if the intersected arc DN is 71º
a
35.5º
b
15.5º
c
20.5º
d
25.5º
e
142º
f
30.5º
2
An svg image showing a math problem
Find angle DRC if the intersected arc DC is 99º
a
44.5º
b
49.5º
c
64.5º
d
59.5º
e
69.5º
f
198º
3
An svg image showing a math problem
Find angle RNZ if the intersected arc RZ is 65º
a
12.5º
b
32.5º
c
130º
d
42.5º
e
52.5º
f
17.5º
4
An svg image showing a math problem
Find angle ZRB if the intersected arc ZB is 59º
a
118º
b
14.5º
c
4.5º
d
9.5º
e
24.5º
f
29.5º
5
An svg image showing a math problem
Find angle RCY if the intersected arc RY is 95º
a
32.5º
b
57.5º
c
190º
d
27.5º
e
47.5º
f
37.5º
6
An svg image showing a math problem
Find angle ZDP if the intersected arc ZP is 83º
a
21.5º
b
61.5º
c
51.5º
d
46.5º
e
166º
f
41.5º
7
An svg image showing a math problem
Find angle PBZ if the intersected arc PZ is 93º
a
46.5º
b
56.5º
c
31.5º
d
186º
e
51.5º
f
41.5º
8
An svg image showing a math problem
Find angle XZN if the intersected arc XN is 99º
a
59.5º
b
29.5º
c
34.5º
d
49.5º
e
198º
f
24.5º