Question

15. Determine the values of the unknown variables.


I'm really just asking how I can get x. From there I can do it I'm just confused in this step

Answer 1

In a triangle, the three interior angles always add to 180°

Step 1  (ΔABD):
x+7 + 3x-18 + x-9 = 180
5x - 20 = 180
5x = 180 + 20
5x = 200
x = 40°

Step 2  (ΔBCD):
x+21 + x+17 + y = 180
2x + 38 + y = 180
2*40 + 38 + y = 180
80 + 38 + y = 180
118 + y = 180
y = 180 - 118
y = 62°