Question

Find the measure of each angle listed below. Enter only numbers without space.

(1) ∠PTQ
(2) ∠QTR
(3) ∠PTS

Answer 1

9514 1404 393

Answer:

1. ∠PTQ = 45°
2. ∠QTR = 15°
3. ∠PTS = 120°

Explanation:

Parallelogram PTSR is divided into two equilateral triangles by diagonal RT. All of the acute angles in that quadrilateral are 60°, and the obtuse angles are 120° (2×60° and also the supplement of 60°).

Triangle PTQ is an isosceles right triangle, so its acute angles are 45°.

∠PTQ = 45°

∠QTR = ∠PTR -∠PTQ = 60° -45°

∠QTR = 15°

∠PTS = 120° . . . . . . obtuse angle in PTSR; sum of ∠PTR and ∠RTS