Inscribed Angles

Question 1

Circle H is inscribed with quadrilateral D E F G. Angle E is 123 degrees. The measure of arc D E is 73 degrees.

Revolt · Accepted Answer

A: 41°

Question 2

Given: Circle M with inscribed and congruent radii JM and MLProve: m =

Revolt · Accepted Answer

C: base angles theorem

Question 3

Given: Circle O with diameter LN and inscribed angle LMNProve: is a right angle.

Revolt · Accepted Answer

B: inscribed angle theorem

Question 4

Given: quadrilateral ABCD inscribed in a circleProve: ∠A and ∠C are supplementary, ∠B and ∠D are supplementaryLet the measure of = a°. Because and form a circle, and a circle measures 360°, the measure of is 360 – a°. Because of the ________ theorem, m∠A = degrees and m∠C = degrees. The sum of the measures of angles A and C is degrees, which is equal to , or 180°. Therefore, angles A and C are supplementary because their measures add up to 180°. Angles B and D are supplementary because the sum of the measures of the angles in a quadrilateral is 360°. m∠A + m∠C + m∠B + m∠D = 360°, and using substitution, 180° + m∠B + m∠D = 360°, so m∠B + m∠D = 180°.What is the missing information in the paragraph proof?

Revolt · Accepted Answer

A: inscribed angle

Question 5

In circle D, angle ADC measures (7x + 2)°. Arc AC measures (8x - 8)°.

Revolt · Accepted Answer

A: 36°

Question 6

Line EF is tangent to circle G at point A.

Revolt · Accepted Answer

C: 190°

Question 7

Angle BAC measures 56°.

Revolt · Accepted Answer

C: 56°

Question 8

Circle F is inscribed with quadrilateral E D C B. Point A is on the circle between points E and B. Angle D E B is 70 degrees and angle D B C is 80 degrees. The measure of arc D C is 88 degrees.

Revolt · Accepted Answer

C: 148°

Question 9

Angle ABD measures (4x + 10)o. Angle ACD measures (5x − 2)o.

Revolt · Accepted Answer

B: 58°

Question 10

Line segment GJ is a diameter of circle L. Angle K measures (4x + 6)°.

Revolt · Accepted Answer

A: 21

Inscribed Angles Answers

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