Inscribed Angle Quadrilateral Circle

15.2 Angles in Inscribed Quadrilaterals

Inscribed Quadrilateral Theorem

If a quadrilateral is inscribed in a circle, then the opposite angles are supplementary.

Multiple Choice

Find a and b.

• a=74 degrees
  b=93 degrees
• a=93 degrees
  b=74 degrees
• a=87 degrees
  b=106 degrees
• a=106 degrees
  b=87 degrees

Multiple Choice

Find the value of d.

• 115

• 65

• 96

• 180

Multiple Choice

Find the value of c.

• 115

• 84

• 96

• 180

Multiple Choice

Find the value of x

• 100

• 105

• 95

• 90

Multiple Choice

Find m∠R.

• 24⁰
• 41⁰
• 67⁰
• 139⁰

Multiple Choice

Quadrilateral ABCD is inscribed in circle O, as shown below.

• x = 85 and y = 50

• x = 90 and y = 45

• x = 110 and y = 75

• x = 115 and y = 70

Multiple Choice

What is the m<B?

• 18

• 115

• 108

• 90

Multiple Choice

If a quadrilateral is inscribed in a circle, then its ____angles are _____.

• adjacent; complimentary

• opposite; complimentary

• adjacent; supplementary

• opposite; supplementary

Multiple Choice

Quadrilateral ABCD is inscribed in the circle. Which sentence is true?

• A and B are supplementary

• A and C are supplementary

• m∠ A = m∠ B

• m∠ C = m∠ D

Multiple Choice

In the diagram below, quadrilateral JUMP is inscribed in a circle..

Opposite angles J and M must be

• right

• complementary

• supplementary

• congruent

Multiple Choice

What is the measure of arc EAB  in circle F?

*HINT: Find ARC CB FIRST THEN 2( ANGLE EDC) =ARC EAB*

• 72

• 92

• 148

• 200

Multiple Choice

What is the measure of arc EAB in circle F?

• 72°

• 92°

• 148°

• 200°

Inscribing a Square in a Circle

• First construct a diameter

• Second construct the perpendicular bisector of the diameter, this will create a second diameter

• Last connect the four endpoints of the two diameters

Multiple Select

Different images of inscribed squares.