RSTU is a square. XWT and SWU are straight lines. SR = SX and ∠WSX = 15°. Find
- ∠SRX
- ∠UTX
.
(a)
∠RSU = 45° (Right angle)
∠RSX
= ∠RSU - ∠WSX
= 45° - 15°
= 30°
∠SRX
= (180° - ∠RSX) ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(b)
SR = SX = ST
XST is an isosceles triangle.
∠SXT = ∠STX (Isosceles triangle)
∠STX
= (180° - ∠UST - ∠WSX) ÷ 2
= (180° - 45° -15°) ÷ 2
= 120° ÷ 2
= 60°
∠UTX
= ∠STU - ∠STX
= 90° - 60°
= 30°
Answer(s): (a) 75°; (b) 30°
