Question

What is the answer for x?

Answer 1

The angle adjacent to 105 that is interior to the triangle is 75 degrees. This is because the two angles must add to 180
105+75 = 180
We can think of it as 105+y = 180 and solve for y to get y = 75
This is the bottom right interior angle of the triangle.

The bottom left interior angle of the triangle is 54 degrees. This angle is a vertical angle paired up with the 54 degree angle already shown.

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The three interior angles of the triangle are: 54, 75, x

For any triangle, the three angles add to 180

54+75+x = 180
129+x = 180
x+129 = 180
x+129-129 = 180-129 ... subtract 129 from both sides
x = 51

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Answer: 51