Geometry Practice Test 1

Question : 39 of 40

Marks: +1, -0

An equilateral triangle TQR is drawn inside a square PQRS. The value of the angle PTS, in degrees, is:

Solution:

In PQRS square, TQR is an equilateral triangle

So, each angle is 60°
∠Q = 90° then ∠PQT = 90° − 60°
So, ∠PQT = 30°
ΔPQT is an isosceles triangle.
∠PQT +∠QTP +∠TPQ = 180°
∠PQT + x° + x° = 180°
2x = 180 − 30°
x =

{150}/2

= 75°
Now ∠PTS in degree = 360° − (75° + 75° + 60°)
= 360° − 210° = 150°

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