Q. 9

$\angle A = (2y + x) \deg \angle B = (33 + x) \deg \angle C = (2y + 10) \deg \angle D = (3x + 5) \deg$

Sum of angles, show that

$7y + 5x = 345$

$\angle A + \angle B + \angle C + \angle D = 360 (2y + x) + (3y + x) + (2y + 10) + (3x + 5) = 360 2y + x + 3y + x + 2y + 10 + 3x + 5 = 360 7y + 5x = 360 - 10 - 5 7y + 5x = 345 \Rightarrow Proved$
Given A = 90 deg then 2y + x = 90

$7y + 5x = 345 2y + x = 90 7y + 5x = 345 10y + 5x = 450 -3y = -105 y = \frac{-105}{-3} y = 35 x = 90 - 2(35) x = 90 - 70 x = 20 (20, 35)$

Find smallest angle

$\angle A = 2(35) + 20 = 70 + 20 = 90 \angle B = 3(35) + 20 = 105 + 20 = 125 \angle C = 2(35) + 10 = 70 + 10 = 80 \angle D = 3(20) + 5 = 60 + 5 = 65 \Rightarrow Answer: D$