In the figure below, x =
A. 37 degrees.
B. 87 degrees.
C. 135 degrees.
D. 145 degrees.
E. 151 degrees.
Since there's no note that says otherwise, we know the figure is drawn to scale. Using visual estimation, we can determine that x > 90. However, a theorem from geometry states that "an exterior angle of a triangle is equal to the sum of the two remote interior angles." So x = 50 + 95, x = 145. Even if you didn't remember the theorem, you know that the sum of the angles of a triangle is 180 degrees. Obviously, then, the unlabeled angle of the triangle must equal 180 - (50 + 95) or 35 degrees. You should also know that angle x and the unlabeled angle in the triangle are supplementary - that is, together they also equal 180 degrees. Therefore, angle x must equal 180 - 35 or 145 degrees.