Inscribed Angles Answers

Line segment XY is tangent to circle Z at point U.

Line segment BD is a diameter of circle E.

Line EF is tangent to circle G at point A.

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

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?

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

Circle O is shown. Angle C A B intercepts arc C B. Arc C B has a measure of 48 degrees.

Angle KJL measures (7x - 8)o. Angle KML measures (3x + 8)o.

Line segment TS is tangent to circle O at point N.

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

Angle BAC measures 56°.

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.

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.

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

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

Line segment BD is a diameter of circle E.

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?

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

Circle G is inscribed with triangle E F D. Point C is on the circle between points E and F. Angle E is 79 degrees. The measure of arc E D is 104 degrees.