QRST is a square. EDS and RDT are straight lines. RQ = RE and ∠DRE = 15°. Find
- ∠RQE
- ∠TSE
.
(a)
∠QRT = 45° (Right angle)
∠QRE
= ∠QRT - ∠DRE
= 45° - 15°
= 30°
∠RQE
= (180° - ∠QRE) ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(b)
RQ = RE = RS
ERS is an isosceles triangle.
∠RES = ∠RSE (Isosceles triangle)
∠RSE
= (180° - ∠TRS - ∠DRE) ÷ 2
= (180° - 45° -15°) ÷ 2
= 120° ÷ 2
= 60°
∠TSE
= ∠RST - ∠RSE
= 90° - 60°
= 30°
Answer(s): (a) 75°; (b) 30°
