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 =
°, m∠q =
°, m∠r =
°

Explanation:

Step1: Recall the definition of acute angles

An acute angle is an angle whose measure is less than \(90^{\circ}\).

Step2: Find a counter - example

Let \(m\angle P = 90^{\circ}\), \(m\angle Q = 45^{\circ}\), \(m\angle R = 45^{\circ}\). Then \(m\angle P+m\angle Q+m\angle R=90^{\circ}+45^{\circ}+45^{\circ}=180^{\circ}\), but \(\angle P\) is not acute (it is a right angle).

Answer:

\(m\angle P = 90^{\circ}\), \(m\angle Q = 45^{\circ}\), \(m\angle R = 45^{\circ}\)