Inscribed Angles Answers

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

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

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

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?