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