Find the value of X

Question

Answer 1

#7

The base angles opposite the two equal sides will be equal (and equal to 47) because the base angle next to 133 form a linear pair. The bottom left angle in the triangle with the bottom right angle of 30 degrees will also be 133 degrees because it is supplementary to a base angle of 47 degrees.

Angle x is an exterior angle which is equal to the sum of the remote two interior angles = 133 + 30 = 163.

#8

The other base angle opposite the two equal sides is 35 so the vertex angle is 180 - 35 - 35 = 110.

That is part of angle x.

Since the top and bottom of the trapezoid are parallel, the other part of angle x is equal to 35 because of alternate interior angles.

so x = 110 + 35 = 145.

Answer 2

Label all angles!

What is a properety of isosceles triangles?