In the figure, ∠KQU is a right-angled isosceles triangle. KU // MT , ∠SPN = 52°, ∠QSR = 37° and ∠NRP = 57°. Find
- ∠KUQ
- ∠PMT
- ∠RTS
(a)
∠KUQ
= (180° - 90°) ÷ 2
= 90° ÷ 2
= 45° (Isosceles triangle)
(b)
∠QSL = 45° (Corresponding angles, UK//SL)
∠PSM
= ∠QSR + ∠QSL
= 37° + 45°
= 82°
∠PMT
= 180° - ∠SPN - ∠PSM
= 180° - 52° - 82°
= 46° (Angles sum of triangle)
(c)
∠RST
= 180° - ∠PSM
= 180° - 82°
= 98°(Angles in a straight line)
∠TRS = ∠PRQ = 57° (Vertically opposite angles)
∠RTS
= 180° - ∠TRS - ∠RST
= 180° - 57° - 98°
= 25° (Angles sum of triangle)
Answer(s): (a) 45°; (b) 46°; (c) 25°
