Question

Secants ⎯⎯⎯⎯⎯⎯⎯⎯⎯ and ⎯⎯⎯⎯⎯⎯⎯⎯ intersect at point T in the interior of a circle. The measure of ∠ is 61.99°. The measure of ⏜ is 70.80°. Determine the measure of ⏜

Answer 1

PR = 53.18°

Explanation:

Given:

m<PTR = 61.99°

arc SQ = 70.80°

Required:

Measure of arc PR

Solution:

Based on the theorem of angles with vertex inside the circle and intercepted arcs, we would have the following equation:

m<PTR = ½(PR + SQ)

Plug in the values

61.99 = ½(PR + 70.80)

Multiply both sides by 2

2*61.99 = PR + 70.80

123.98 = PR + 70.80

123.98 - 70.80 = PR

53.18 = PR

PR = 53.18°