Question

In the figure below, AB = AC and BC is extended to D, then find the value of x + y
(1) 120°
(2) 160°
(3) 40°
(4) 144°
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Answer 1

Step-by-step explanation:

Since AB = AC,

angle B = angle C (angles opposite to equal sides are equal)NOTE : angle c is only the angle inside the triangle...

Then angle c = 2x

Angle A + Angle B + Angle c = 180 ( sum of angles in a triangle);

x + 2x + 2x = 180

5x = 180

x = 36

therefore x (angle A) = 36 degrees

Angle B = 2x = 2 x 36 = 72 degrees

Angle C = Angle B = 72 degrees

Angle B + Angle Y = 180 (angles in straight line)

72 + Y = 180

Y = 180 - 72

Y = 108 degrees

X + Y = 36 degrees + 108 degrees

= 144 degrees

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Answer 2

Ans is 144degree option 4