Solve for x using the exterior angle theorem. show your work.

To find X, we need to first find at least two angles of the triangle (This is because triangles will always have angles that add up to 180 degrees).

Now, since the angle of 135 has a linear pair, we can set 135 + A(the unknown angle) = 180 as so:

135 + A = 180

Solve for A:

Subtract 135 on each side,
135 - 135 + A = 180 - 135
A = 45

Awesome! Now we have the two angles of the triangle. (77 and 45 degrees).
Remember: the angles of a triangle add up to be 180.

We can now set up an equation as so:

77 + 45 + X = 180
122 + X = 180

Solve for X,
Subtract 122 on each side:

122 - 122 + X = 180 - 122
X = 58

Sweet! We found what angle X is. To check our work we can add all the angles and see if they do indeed equal 180.

77 + 45 + 58 = 180
122 + 58 = 180
180 = 180

So we have found out X is definitely 58 degrees.

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