Inscribed Triangle on Diameter - Missing Angle (Level 1)

This math topic focuses on the geometry of circles, specifically working with inscribed triangles where one side is the diameter. The main skill practiced is solving for missing angles within these triangles. Each problem presents a different triangle inscribed in a circle, with one angle given and the student required to find another. The problems invite the student to apply the theorem that a triangle inscribed in a circle and subtended by the diameter is a right triangle. Various angle values are presented in a multiple-choice format for students to select the correct answer.

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

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Geometry of Circles - Inscribed Triangle on Diameter - Missing Angle Worksheet

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Geometry of Circles - Inscribed Triangle on Diameter - Missing Angle
1
An svg image showing a math problem
Find angle PDC in degrees given that PCD is 50º and DC forms a diameter
a
10º
b
115º
c
55º
d
85º
e
100º
f
40º
2
An svg image showing a math problem
Find angle MCB in degrees given that MBC is 30º and CB forms a diameter
a
b
60º
c
75º
d
150º
e
15º
f
135º
3
An svg image showing a math problem
Find angle MCZ in degrees given that MZC is 50º and CZ forms a diameter
a
100º
b
130º
c
40º
d
20º
e
115º
f
35º
4
An svg image showing a math problem
Find angle DZM in degrees given that DMZ is 30º and ZM forms a diameter
a
45º
b
75º
c
60º
d
105º
e
15º
f
135º
5
An svg image showing a math problem
Find angle NPD in degrees given that NDP is 70º and PD forms a diameter
a
110º
b
25º
c
20º
d
80º
e
35º
f
50º
6
An svg image showing a math problem
Find angle BPY in degrees given that BYP is 40º and PY forms a diameter
a
50º
b
20º
c
80º
d
e
125º
f
110º
7
An svg image showing a math problem
Find angle CRB in degrees given that CBR is 50º and RB forms a diameter
a
10º
b
20º
c
d
115º
e
40º
f
35º
8
An svg image showing a math problem
Find angle ZYR in degrees given that ZRY is 70º and YR forms a diameter
a
65º
b
20º
c
95º
d
50º
e
25º
f
35º