Answer:
x = 20, y = 70 degrees.
Step-by-step explanation:
x + y = 90 degrees ( As the large triangle is right-angled).
Now x is the base angle of an isosceles triangle so the small angle that is part of the right angle = x. Call this angle z.
Consider the small triangle which includes 40 degrees:
y + 40 + 90 - z = 180 But as z = x:
y + 130 - x = 180
y - x = 50
Adding the equation to the highlighted equation above we have:
2y = 90 + 50
2y = 140
y = 70 degrees.
So x + 70 = 90
giving x = 20 degrees.
