Question

Circle P is divided into four central angles by the diameters AC and BD.

The four central angles are ZAPB, ZBPC, ZCPD, and ZAPD.
The measure of ZAPD is (x + 1)º and the measure of ZAPB is (3x-18)º.
Find the measure of ZCPD to the nearest hundredth of a degree.

Answer 1

m∠CPD = 129.75°

Explanation:

m∠APD + m∠APB = 180 since the angles are supplementary

x + 1 + 3x - 18 = 180

4x - 17 = 180

4x = 197

x = 49.25

m∠APB = 3(49.25) - 18 = 129.75

m∠APB = m∠CPD because the angles are vertical angles

m∠CPD = 129.75°