Answer:
x = 7.5°
Y = 75°
Step-by-step explanation:
∵ ΔMNO is equilateral triangle
∴ M∠MNO = 60°
∴ 2x + 4x + 2x = 60°
∴ 8x = 60 ⇒ ∴ x = 60/8 = 7.5°
In the 2Δ which contain NM , NO and angles 2x° , 2x°
∵ MN = ON ⇒ equilateral Δ
∵ 2x° = 2x° = 15°
∵ m∠M = m∠O = 60 ⇒ equilateral Δ
∴ 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°
