QRST is a square. TSS and RST are straight lines. RQ = RT and ∠SRT = 15°. Find
- ∠RQT
- ∠TST
.
(a)
∠QRT = 45° (Right angle)
∠QRT
= ∠QRT - ∠SRT
= 45° - 15°
= 30°
∠RQT
= (180° - ∠QRT) ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(b)
RQ = RT = RS
TRS is an isosceles triangle.
∠RTS = ∠RST (Isosceles triangle)
∠RST
= (180° - ∠TRS - ∠SRT) ÷ 2
= (180° - 45° -15°) ÷ 2
= 120° ÷ 2
= 60°
∠TST
= ∠RST - ∠RST
= 90° - 60°
= 30°
Answer(s): (a) 75°; (b) 30°
