Question

show that the conjecture is false by providing a counterexample.
if the measures of ∠r, ∠s, and ∠t sum to 180°, then one of the angles must be obtuse.
counterexample:
m∠r = □°, m∠s = □°, m∠t = □°

Explanation:

Step1: Recall the definition of obtuse angle

An obtuse angle is an angle whose measure is greater than \(90^{\circ}\) and less than \(180^{\circ}\).

Step2: Choose non - obtuse angles

Let \(m\angle R = 60^{\circ}\), \(m\angle S=60^{\circ}\), \(m\angle T = 60^{\circ}\).

Step3: Check the sum

\(m\angle R+m\angle S + m\angle T=60^{\circ}+60^{\circ}+60^{\circ}=180^{\circ}\)

Answer:

\(m\angle R = 60^{\circ}\), \(m\angle S = 60^{\circ}\), \(m\angle T = 60^{\circ}\)