Chapter 4 exercise 8

Let ABCD be a convex cyclic quadrilateral. Prove angle A and C are supplemetary- proved in exercise 1h. Prove that the exterior angle at B is congruent to the interior angle at D. The alternate interior angles B and D are supplementary as proved in 8a. Construct line AB. The interior angle B and exterior angle B are supplementary because they create a straight line. Thus measure D+ measure B=180. And measure of CBE+ measure B=180. Hence, measure of D + measure B= measure CBE+ measure B. Measure D= measure CBE. Therefore the interior measure D is congruent to exterior angle B. Angle A and C are congruent. B and D become supplementary.