The angles of a triangle x, y, and z are in descending order.

If 2x − y = 100° = 3y − 2z, its smallest angle is:

Correct option is D

Given:

2x − y = 100° and 3y − 2z = 100°
Also, x + y + z = 180° (sum of angles in a triangle)
Angles are in descending order: x > y > z

Formula:
Use algebraic substitution and angle sum property.

Solution:
From 2x − y = 100 → y = 2x − 100 — (i)
From 3y − 2z = 100 → z = (3y − 100)/2 — (ii)

Now using x + y + z = 180
Substitute (i) and (ii):
x + (2x − 100) + [(3(2x − 100) − 100)/2] = 180
x + 2x − 100 + [(6x − 300 − 100)/2] = 180
3x − 100 + (6x − 400)/2 = 180
3x − 100 + 3x − 200 = 180
6x − 300 = 180 → 6x = 480 → x = 80°
Then y = 2x − 100 = 160 − 100 = 60°
Then z = (3y − 100)/2 = (180 − 100)/2 = 40°

Final Answer: (d) 40°