High School

In triangle PQR, bisector QS splits angle PQR, which has a measure of 124 degrees. Find the measures of angles PQS and ZRQS.

A) m∠PQS = 62 degrees, m∠ZRQS = 62 degrees
B) m∠PQS = 62 degrees, m∠ZRQS = 124 degrees
C) m∠PQS = 124 degrees, m∠ZRQS = 62 degrees
D) m∠PQS = 124 degrees, m∠ZRQS = 124 degrees

Answer :

Final answer:

Angle bisector QS divides angle PQR into two equal angles of 62 degrees each. Therefore, the measures of angles PQS and ZRQS are both 62 degrees, making option (a) correct mPQS = 62 degrees, mZRQS = 62 degrees.

Explanation:

In triangle PQR, the angle bisector QS divides angle PQR into two equal parts. Since the measure of angle PQR is given as 124 degrees, each of the two equal parts will be half of 124 degrees. Therefore, the measure of angle PQS is 124/2, which is 62 degrees.

The measure of angle ZRQS would be the same as angle PQS, assuming that ZRQS refers to the angle formed on the opposite side of the bisector but within the same plane, hence it is also 62 degrees.

Thus, the correct option is: (a) mPQS = 62 degrees, mZRQS = 62 degrees

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