Answer:
e = 126
Step-by-step explanation:
Both triangles are isosceles triangles. Therefore in the smaller triangle, there are two angles that are equal to 42 degrees (the other one is next to e)
42 + 42 = 84
there are 180 degrees in a triangle
180 - 84 = 96
So the last angle in the triangle (The little one) is equal to 96 degrees.
The rule for cyclic quadrilaterals is that the two opposite angles equal 180. So the angle opposite 96 degrees will be equal to:
180 - 96 = 84
As the larger triangle is also an isosceles (as mentioned above), two angles will be equal to each other. The two angles that are equal are at the bottom left. As one of them is equal to 84, the other is also equal to 84. This means the last angle (the one at the top) is equal to:
180 - (84 + 84) =
180 - 168 = 12
Angles on a straight line always equal 180 degrees. So 'e' is equal to 180 minus the other two triangle angles on the line they all share.
180 - (12 + 42) =
180 - 54 = 126
Therefore e = 126
