The correct option is A 40
Given: AB || BC and AB = AC
△ABC is an isosceles triangle as its two sides are equal in length.
∴ y = z {Angles opposite to equal sides of an isosceles triangle are equal}
In △ABC,
x + y + z = 180∘
x + 2y = 180∘ ...(i)
∠EAD + ∠DAB + ∠BAC = 180∘
{Angles on a straight line}
55∘ + x + ∠DAB = 180∘
∵ AD || BC, ∠DAB = y
∴ 55∘ + x + y = 180∘
x +y =125 ...(ii)
Solving (i) and (ii)
x + 2y = 180∘
2x + 2y = 250
- - -
--------------------------
-x = -70
--------------------------
⇒x=70∘
⇒y=125−x=55∘
⇒z=y=55∘
∴ x, y and z are 70∘, 55∘ and 55∘ respectively.
Then, y+z-x = 55∘ + 55∘ - 70∘ = 110∘ - 70∘ = 40∘