Verified answer

Step-by-step explanation:

Given: PQRS is a rectangle, the perpendicular ST from S on PR divides angle S in the ratio 2 : 3.

To find: Here we have to find the value of the angle TPQ.

∠ PSR = 90°

It is given that, the perpendicular ST from S on PR divides angle S in the ratio 2 : 3

Divide the 90° angle into the ratio 2 : 3.

2x+3x=90°

5x = 90°

Therefore,x=18°

2x= 2*18=36°

3x=3*18=54°

So,

∠ PST = 36

Now, in ∠†PST;

∠ PST +∠ PTS +∠ TPS = 180° (Sum of all angles of a triangle)

36° + 90°+ ∠ TPS = 180°

∠ TPS = 180° -36° -90°

∠ TPS = 54°

Now,

∠ TPQ = ∠ SPQ ∠ TPS

∠ TPQ = 90° -54°

∠ TPQ = 36°

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