Question

in △opq, pq = 10, qo = 4, and op = 11. which statement about the angles of △opq must be true? answer: m∠q > m∠p > m∠o; m∠p > m∠q > m∠o; m∠o > m∠p > m∠q; m∠q > m∠o > m∠p; m∠p > m∠o > m∠q; m∠o > m∠q > m∠p

Explanation:

Step1: Recall angle - side relationship

In a triangle, the larger the side length, the larger the measure of the opposite angle.

Step2: Identify side - angle pairs

In \(\triangle OPQ\), side \(OP = 11\) is opposite \(\angle Q\), side \(PQ=10\) is opposite \(\angle O\), and side \(QO = 4\) is opposite \(\angle P\).

Step3: Compare side lengths

We have \(OP> PQ>QO\).

Step4: Determine angle - measure order

Since \(OP> PQ>QO\), then \(m\angle Q>m\angle O>m\angle P\) (by the angle - side relationship in a triangle).

Answer:

\(m\angle Q>m\angle O>m\angle P\)