Question

In the figure shown, BC is produced to D. Find the value of x+y.
(A) 135
(B) 140
(C) 145
(D) 130​

Answer 1

Answer:

The value of x + y = 135°

Step-by-step explanation:

In the figure, it is shown that the triangle is an isosceles triangle.

The given angles of the triangle are 2y and 3y. The third angle must be 3y because it is an isosceles triangle.

The sum of the three interior angles of a triangle is 180 degrees. Then,

  2y + 3y + 3y = 180°

  8y = 180°

   $y=\dfrac{180}{8}=22.5^\circ$

∴  $3y=3\times 22.5 = 67.5^\circ$

We know that the sum of an interior angle and its adjacent exterior angle is 180 degrees. Therefore,

  67.5°+ x = 180°

Then, x = 180° - 67.5°

          = 112.5°

Now we have the values of x and y.

Hence, x + y = 112.5° + 22.5°

                 = 135°

Answer 2

Step-by-step explanation:

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