Secants, Tangents, and Angles Answers

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

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

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

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

Line segment BD is a diameter of circle E.

Angle BAC measures 56°.

Line EF is tangent to circle G at point A.