QRST is a square. JHS and RHT are straight lines. RQ = RJ and ∠HRJ = 13°. Find
- ∠RQJ
- ∠TSJ
.
(a)
∠QRT = 45° (Right angle)
∠QRJ
= ∠QRT - ∠HRJ
= 45° - 13°
= 32°
∠RQJ
= (180° - ∠QRJ) ÷ 2
= (180° - 32°) ÷ 2
= 148° ÷ 2
= 74° (Isosceles triangle)
(b)
RQ = RJ = RS
JRS is an isosceles triangle.
∠RJS = ∠RSJ (Isosceles triangle)
∠RSJ
= (180° - ∠TRS - ∠HRJ) ÷ 2
= (180° - 45° -13°) ÷ 2
= 122° ÷ 2
= 61°
∠TSJ
= ∠RST - ∠RSJ
= 90° - 61°
= 29°
Answer(s): (a) 74°; (b) 29°
