Find x and y in the illustration below

Question

 D  y*                 C       *=degrees 

    _____________

   /                      /

  /                      /

 /___________  /

 

A  (2x + y)*        B  3x*

 

Answer 1

This looks like a parallelogram, and these quadrilaterals have special features. One is that opposite angles are congruent, and another is that consecutive angles add up to 180 degrees.

 

y & 3x are opposite angles so y = 3x

 

(2x + y) & y are consecutive angles so they add up to 180 degrees. 

 

2x + 2y = 180

 

Substitute

 

2x + 2(3x) = 180

 

8x = 180

 

x = 45/2

 

y = 3 * 45/2 = 135/2