Question

I need help please. Thanks

Answer 1

Given:

m∠APD = (7x + 1)°

m∠DPC = 90°

m∠CPB = (9x - 7)°

To find:

The measure of arc ACD.

Solution:

Sum of the adjacent angles in a straight line = 180°

m∠APD + m∠DPC + m∠CPB = 180°

7x° + 1° + 90° + 9x° - 7° = 180°

16x° + 84° = 180°

Subtract 84° from both sides.

16x° + 84° - 84° = 180° - 84°

16x° = 96°

Divide by 16° on both sides.

x = 6

m∠APB = 180°

m∠BPD = (9x - 7)° + 90°

             = (9(6) - 7)° + 90°

             = 47° + 90°

m∠BPD = 137°

m∠APD = m∠APB + m∠BPD

             = 180° + 137°

             = 317°

The measure of the central angle is congruent to the measure of the intercepted arc.

m(ar ACD) = m∠APD

m(ar ACD) = 317°

The arc measure of ACD is 317°.