Geometry of Circles - 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.

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

Math worksheet on 'Geometry of Circles - Inscribed Triangle on Diameter - Missing Angle (Level 1)'. Part of a broader unit on 'Geometry - Intermediate - Intro' Learn online: app.mobius.academy/math/units/geometry_intermediate_intro/

1

Find angle DCX in degrees given that DXC is 20º and CX forms a diameter

a

85º

b

145º

c

70º

d

5º

e

160º

f

130º

2

Find angle YBR in degrees given that YRB is 30º and BR forms a diameter

a

30º

b

75º

c

15º

d

150º

e

60º

f

135º

3

Find angle DNC in degrees given that DCN is 70º and NC forms a diameter

a

35º

b

5º

c

40º

d

10º

e

80º

f

20º

4

Find angle CND in degrees given that CDN is 60º and ND forms a diameter

a

45º

b

60º

c

90º

d

15º

e

0º

f

30º

5

Find angle ZNC in degrees given that ZCN is 30º and NC forms a diameter

a

45º

b

90º

c

60º

d

120º

e

150º

f

15º

6

Find angle CNM in degrees given that CMN is 20º and NM forms a diameter

a

85º

b

130º

c

145º

d

10º

e

70º

f

5º

7

Find angle BPY in degrees given that BYP is 30º and PY forms a diameter

a

15º

b

90º

c

150º

d

120º

e

60º

f

105º