Answer: x = 31
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Explanation:
Refer to the diagram below. I've added the variable y as the base angles to the isosceles triangle on the left.
Recall that the angles opposite the congruent sides are the base angles. The base angles of any isosceles triangle are the same measure.
Let's solve for y
y+y+56 = 180 .... all angles in a triangle add to 180
2y+56 = 180
2y = 180-56
2y = 124
y = 124/2
y = 62
I've also added the variable z, which is adjacent to one of the y angles.
Since y and z combine to form a straight angle, this means the two angles add to 180
y+z = 180
z = 180-y
z = 180-62
z = 118
Now focus on the isosceles triangle on the right. It has angles x, x, and z = 118.
x+x+z = 180
x+x+118 = 180
2x+118 = 180
2x = 180-118
2x = 62
x = 62/2
x = 31
