Question

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Answer 1

It is given that QS bisects ∠PQR. So, ∠PQS ≈ ∠SQR by the definition of the term bisect. Therefore, m∠PQS = m∠SQR by the angle congruence postulate. It is given that m∠PQS is 45°, so 45° = m∠SQR by the Linear Pair Postulate property of equality. m∠PQS + m∠SQR = m∠PQR by the Angle Additional Postulate, so 45° + 45° = m∠PQR by the substitution property of equality, and simplifying gives 90° = m∠PQR. Therefore, ∠PQR is a right angle angle by the definition of the term right angle.