Question

7. In the diagram shown, PT = QT = QR.

Also, RT = RS and PTQ = 36º.
What is PTS?
A 72°, B 80°, C 90°, D 100°, E 108°
Please can anyone help me understand this question??

Answer 1

C

Explanation:

Since PT = QT , then Δ PQT is isosceles with the 2 base angles congruent.

∠ PQT =
`(180-36)/(2)` = 72°

∠ TQR = 180° - 72° = 108° ( adjacent angles on a straight line )

Since QT = QR , then Δ QRT is isosceles with 2 base angles congruent

∠ QTR = ∠ QRT =
`(180-108)/(2)` =
`(72)/(2)` = 36°

∠ TRS = 180° - 36° = 144° ( adjacent angles on a straight line )

Since RT = RS , then Δ TRS is isosceles with 3 bas angle congruent

∠ RTS = ∠ RST =
`(180-144)/(2)` =
`(36)/(2)` = 18°

Then

∠ PTS = ∠ PTQ + ∠ QTR + ∠ RTS = 36° + 36° + 18° = 90°