 ## Question

primary 6 | Maths | Geometry

Anyone can contribute an answer, even non-tutors.

##### Cindy

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Date Posted: 4 months ago
Views: 34
J
4 months ago
QR = TR
△QRT is isosceles.

QR also = SR (both are sides of a square)

So TR = SR
△ SRT is also isosceles

Use the properties of an isosceles triangle to solve
Cindy
4 months ago
Thank you very much.
J
4 months ago
You're welcome

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Date Posted: 4 months ago
Hooi Ying Xuan
4 months ago
According to question, QR = TR. and since PQRS is a square, QR = RS too. Therefore, QR = TR = RS, which makes the angle RTS = angle RST.
J
4 months ago
The second part of your working is incorrect. The two triangles are isosceles, but they are not neither similar nor congruent.

Angle TRS cannot be 40° as the sum of angle TRS and angle QRT (which gives QRS) would then be 80°, but QRS is actually a right angle (90°), which is a contradiction.

angle TRS = angle QRS - angle QRT
= 90° - 40°
= 50°

Angle RST = (180° - 50°)/2 = 65°
Hooi Ying Xuan
4 months ago
Apologies, I labeled 40* at the wrong location causing the mistake. It should be 90* - 40* = 50* then 180* - 50* = 130* divide by 2 = 65*.
Cindy
4 months ago
Thank you. 