x = 7.5° and y = 75°
Solution:
ΔMNO is equilateral triangle.
Each angle in equilateral triangle is 60°.
⇒ m∠MNO = 60°
⇒ 2x° + 4x° + 2x° = 60°
⇒ 8x° = 60°
Divide by 8 on both sides.
⇒ x° = 7.5°
In the 2 triangles which contain NM , NO and angles 2x° , 2x°
MN = ON ⇒ equilateral triangle
∵ 2x° = 2x° = 15°
m∠M = m∠O = 60° ⇒ equilateral triangle
∴ The two triangles are congruent.
The third angles in the two triangles are equal and their measure is
180 – (60 + 15) = 105°
105 + y° = 180 ⇒ straight angle
y° = 180 – 105 = 75°
y° = 75°
Hence x = 7.5° and y = 75°.
