ANSWER
x = 30 degrees and y = 5
EXPLANATION
The figure is made up of two triangles: one is equilateral and the other is isoceles.
The equilateral triangle is:
It is equilateral because the three angles are equal. This means that the three sides are of equal length as well.
So:
8y = 40
Divide through by 8:
y = 40 / 8
y = 5
The second triangle is given below. Let us label it as such:
The angle So, we have that:
Since the triangle is isoceles, it means that two sets of angles are equal (and two sets of sides are equal):
The sum of angles in a triangle is 180 degrees, so:
x + x + 120 = 180
2x = 180 - 120 = 60
Divide through by 2:
x = 60 / 2
x = 30 degrees
So, x = 30 degrees and y = 5
