Inscribed Angles: Practice Level 2 | Geometry

Level 2 · Intermediate 0 / 12 answered

Question 1 of 12

1

Diameter $VD$ lies inside $\angle AVB$ . On the intercepted arc, $AD$ measures $42^\circ$ and $DB$ measures $118^\circ$ . Find $m\angle AVB$ .

Answer choices for question 1 A $38^\circ$ B $160^\circ$ C $80^\circ$ D $59^\circ$
2

Diameter $VD$ is outside $\angle AVB$ . Along the arc away from $V$ , the order is $D,A,B$ . Arc $DB$ measures $162^\circ$ and $DA$ measures $48^\circ$ . Find $m\angle AVB$ .

Answer choices for question 2 A $57^\circ$ B $105^\circ$ C $114^\circ$ D $81^\circ$
3

$VA$ is a diameter through center $O$ , and $m\angle VOB=108^\circ$ . Find $m\angle AVB$ .

Answer choices for question 3 A $54^\circ$ B $72^\circ$ C $108^\circ$ D $36^\circ$
4

$P,Q$ lie on the same open arc between $A,B$ . The angles $APB$ and $AQB$ measure $(2x+13)^\circ$ and $(4x-17)^\circ$ . Find $x$ .

Answer choices for question 4 A $2$ B $15$ C $30$ D $7.5$
5

$P,R$ lie on opposite open arcs between $A,B$ . Their inscribed angles measure $(3x+4)^\circ$ and $(5x+8)^\circ$ . Find $x$ .

Answer choices for question 5 A $21$ B $-2$ C $22.5$ D $42$
6

Triangle $ACB$ is inscribed in a circle with diameter $AB$ . Given $m\angle CAB=29^\circ$ , find $m\angle ABC$ .

Answer choices for question 6 A $29^\circ$ B $61^\circ$ C $90^\circ$ D $151^\circ$
7

Triangle $ABC$ is inscribed in a circle. Its angle at $A$ is $24^\circ$ , and its angle at $B$ is $66^\circ$ . Which segment must be a diameter?

Answer choices for question 7 A $AC$ B $BC$ C $AB$ D No segment is forced to be a diameter
8

Minor arc $TA$ measures $154^\circ$ . Ray $TS$ is tangent at $T$ on the opposite side of line $OT$ from $A$ . Find $m\angle STA$ .

Answer choices for question 8 A $77^\circ$ B $26^\circ$ C $154^\circ$ D $103^\circ$
9

Ray $TR$ is tangent at $T$ on the same side of line $OT$ as $A$ . Given $m\angle RTA=46^\circ$ , find the measure of minor arc $TA$ .

Answer choices for question 9 A $23^\circ$ B $134^\circ$ C $268^\circ$ D $92^\circ$
10

A tangent-chord angle measures $127^\circ$ . What are the measure and type of its intercepted arc?

Answer choices for question 10 A $106^\circ$ , minor B $254^\circ$ , minor C $254^\circ$ , major D $106^\circ$ , major
11

Diameter $VD$ lies inside $\angle AVB$ , with $D$ on its intercepted arc. Let $a$ be the measure of arc $ADB$ , $b$ the measure of arc $AD$ , and $c$ the measure of arc $DB$ . Which equation correctly assembles the arc?

Answer choices for question 11 A $a=b+c$ B $a=b-c$ C $a=\tfrac12b+\tfrac12c$ D $a=360^\circ+b+c$
12

Points $A,P,B,Q$ occur in order around a circle. Arc $APB$ measures $(3x+24)^\circ$ , and arc $AQB$ measures $(5x+16)^\circ$ . Find $m\angle APB$ .

Answer choices for question 12 A $72^\circ$ B $108^\circ$ C $144^\circ$ D $216^\circ$