QRST is a square. CBS and RBT are straight lines. RQ = RC and ∠BRC = 13°. Find
- ∠RQC
- ∠TSC
.
(a)
∠QRT = 45° (Right angle)
∠QRC
= ∠QRT - ∠BRC
= 45° - 13°
= 32°
∠RQC
= (180° - ∠QRC) ÷ 2
= (180° - 32°) ÷ 2
= 148° ÷ 2
= 74° (Isosceles triangle)
(b)
RQ = RC = RS
CRS is an isosceles triangle.
∠RCS = ∠RSC (Isosceles triangle)
∠RSC
= (180° - ∠TRS - ∠BRC) ÷ 2
= (180° - 45° -13°) ÷ 2
= 122° ÷ 2
= 61°
∠TSC
= ∠RST - ∠RSC
= 90° - 61°
= 29°
Answer(s): (a) 74°; (b) 29°
