Question

A conjecture and the flowchart proof used to prove the conjecture are shown.

Answer 1

Okay. An obtuse triangle is any triangle that has 1 angle that measures more than 90°. As we can see, angle QRS measures 76° and angle PRQ measures 104°. 104 > 90. Triangle PQR is a closed figure, and a triangle measures 180° total. There can only be 1 obtuse angle in any triangle. PRQ is an obtuse angle. Therefore, triangle PQR is an obtuse triangle.

Answer 2

Answer:-

Given: m∠QRS=76°

Prove: △PQR is an obtuse triangle.

Proof:- ∠ORS=76° [given]

∠PRQ and ∠QRS are supplementary . [Linear pair postulate.]

m∠PRQ+76°=180° [Substitution property of equality]

m∠PRQ=104°  [Subtraction property of equality]

∠PRQ is an obtuse angle [Definition of obtuse angle]

ΔPQR is an obtuse triangle.[Definition of obtuse triangle]