Inscribed Triangle on Diameter - Missing Angle (Level 2)

This math topic focuses on solving problems related to inscribed triangles in circles, where one side of the triangle is a diameter. Specifically, it involves finding the missing angle of the triangle using properties from circle geometry. Each question presents a triangle with one known angle and requires calculating the second angle, exploiting the theorem that an angle inscribed in a semicircle is a right angle (90 degrees). The topic is suitable for learners at an intermediate level in geometry.

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 RYX in degrees given that RXY is 35º and YX forms a diameter
a
55º
b
25º
c
115º
d
20º
e
145º
f
10º
2
An svg image showing a math problem
Find angle MND in degrees given that MDN is 55º and ND forms a diameter
a
10º
b
35º
c
20º
d
25º
e
50º
f
3
An svg image showing a math problem
Find angle DCP in degrees given that DPC is 25º and CP forms a diameter
a
155º
b
140º
c
95º
d
20º
e
10º
f
65º
4
An svg image showing a math problem
Find angle MYD in degrees given that MDY is 65º and YD forms a diameter
a
35º
b
10º
c
20º
d
e
25º
f
55º
5
An svg image showing a math problem
Find angle YZC in degrees given that YCZ is 55º and ZC forms a diameter
a
110º
b
25º
c
95º
d
125º
e
80º
f
35º
6
An svg image showing a math problem
Find angle BMX in degrees given that BXM is 45º and MX forms a diameter
a
135º
b
45º
c
105º
d
30º
e
60º
f
15º
7
An svg image showing a math problem
Find angle BYZ in degrees given that BZY is 25º and YZ forms a diameter
a
155º
b
65º
c
110º
d
20º
e
140º
f
8
An svg image showing a math problem
Find angle DZP in degrees given that DPZ is 55º and ZP forms a diameter
a
65º
b
125º
c
35º
d
e
20º
f
50º