Question

9. Consider the diagram below. First, solve for x, then y.

Answer 1

y = 32; x = 59

Explanation:

On the top triangle x+y+89=180 because a triangle's angles add up to 180 degrees, while a quadrilateral's angles add up to 360 degrees.

Angle 89 and the angle below it are supplementary, meaning together they equal 180 degrees.

180 - 89 = 91

So the angle below 89 is 81 degrees.

Now we can subtract the other three angles in the quadrilateral to find the fourth:

360 - (78 + 43 + 91) = 148

So the angle below y is 148 degrees.

Angle y and the angle below it are supplementary, meaning together they equal 180 degrees.

y = 180 - 148

y = 32

All of the angles in a triangle equal 180 degrees:

x = 180 - (32 + 89)

x = 59

Answer 2

x = 59

y = 32

Explanation:

x + 78 + 43 = 180

x = 59

y + 59 + 89 = 180

y = 32