x = 7.5° and y = 75°
Solution:
ΔMNO is equilateral triangle.
Each angle in equilateral triangle is 60°.
m∠MNO = 60°, m∠NOM = 60°, m∠NMO = 60°
⇒ m∠MNO = 60°
⇒ 2x° + 4x° + 2x° = 60°
⇒ 8x° = 60°
Divide by 8 on both sides of the equation.
⇒ x° = 7.5°
In the triangles which contain NM and NO, angles are 2x° , 2x°.
2x° = 2(7.5°) = 15°
In small triangle which contain NO,
60° + 2x° + unknown side = 180°
60° + 15° + unknown side = 180°
75° + unknown side = 180°
unknown side = 180° – 75°
unknown side = 105°
The unknown side of small triangle which contain NO = 105°
This side and y° forms a linear pair.
y° + 105° = 180°
y° = 180° – 105°
y° = 75°
Hence x = 7.5° and y = 75°.
