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Find the angle given in the problem below...



Find angle QPR

Find the angle given in the problem below... Find angle QPR-example-1

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By applying the angle bisector theorem, the measure of angle QPR is equal to 25°.

In Mathematics and Euclidean Geometry, an angle bisector is a type of line, ray, or segment, that typically divides or bisects a line segment exactly into two (2) equal and congruent angles.

Based on the definition of angle bisector, we can logically deduce that angle GFH is congruent with angle EFH;

m∠QPS = m∠RPS + m∠QPR

By using the substitution method, we have:

40 = 8x + 7 + 9x + 16

40 = 17x + 23

17x = 40 - 23

x = 17/17

x = 1

For the measure of angle QPR, we have;

m∠QPR = 9x + 16

m∠QPR = 9(1) + 16

m∠QPR = 25°

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