Question

show that the conjecture is false by providing a counterexample: if the measures of ∠p, ∠q, and ∠r sum to 180°, then all of the angles must be acute. counterexample: m∠p = 0°, m∠q = 0°, m∠r = 0°

Explanation:

Step1: Recall definition of acute angle

An acute angle has measure less than 90°.

Step2: Create counter - example

Let \(m\angle P = 30^{\circ}\), \(m\angle Q= 60^{\circ}\), \(m\angle R = 90^{\circ}\). We have \(m\angle P+m\angle Q + m\angle R=30^{\circ}+60^{\circ}+90^{\circ}=180^{\circ}\), but \(\angle R\) is a right - angle (not acute).

Answer:

\(m\angle P = 30\), \(m\angle Q = 60\), \(m\angle R = 90\)