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Serjik [45]
3 years ago
13

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 ⏜

Mathematics
1 answer:
kiruha [24]3 years ago
4 0

Answer:

PR = 53.18°

Step-by-step 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°

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