Question

Find the measure of arc PS

Answer 1

• 142°

--------------------

Both angles PQS and PRS intercept same arc PS, hence they have same measure:

• m∠PQS = m∠PRS

Substitute values and solve for x:

• 5x + 1 = 8x - 41
• 8x - 5x = 1 + 41
• 3x = 42
• x = 14

Plug in the value of x into either angle measure:

• m∠PQS = 5*14 + 1 = 71°

The intercepted arc is twice the inscribed angle measure:

• mPS = 2*m∠PQS
• mPS = 2*71°
• mPS = 142°