In the figure above, AD intersects BE at C. If x = 100, what is the value of y ?

The correct answer is: 80

○        The sum of angles of triangle is 180^o.
○        Vertically opposite angles are equal.

• Step by step explanation:

○        Given:
○        In △ABC,
∠BAC = 20^o
∠ABC = x^o
x^o = 100
In △CDE,
∠DEC = 40^o
∠CDE = y^o
○        Step 1.
○        Find ∠ACB,
In  △ABC,
∠ABC + ∠ACB + ∠CAB = 180   ( ∵ sum of angle of triangle = 180^o)
x + 20 + ∠ACB = 180
100 + 20 + ∠ACB = 180
120 + ∠ACB = 180
∠ACB = 180 - 120
∠ACB = 60^o
∴ ∠ACB = 60^o.
○        Step 2:
○        Find ∠DCE,
∠DCE = ∠ACB        ( ∵ vertically opposite angle )
∠DCE = 60^o
○        Step 3:
○        Find y,
In  △CDE,
∠CDE + ∠CED + ∠DCE = 180   ( ∵ sum of angle of triangle = 180^o)
y + 40 + 60 = 180
y + 100 = 180
y = 180 - 100
y = 80
∠CDE = 80^o
∴ y = 80^o.

• Final Answer:

Correct option is,
Option C. 80^o.