Exterior Angle of a Triangle Example

Question:
In the figure below, points A, B, C lie on a straight line, DBC is a triangle. If the angle ABD is 136o, what is the value of x?
triangle exterior angles example
Solution:
Since points A, B, and C lie on a straight line, so angle ABD is an exterior angle of triangle DBC
angle ABD = angle D + angle C (Exterior angle of a triangle theorem)
Given: angle D = xo and angle C = xo
136 = x + x
2x = 136
x = 68
The value of x is 68.

When extended one side of a triangle, an exterior angle of a triangle is formed. The exterior angle of a triangle is equal to the sum of two noadjacent interior angles. In this problem, we get angle ABD = angle D + angle C. Given angle ABD is 136o, then x + x = 136. 2x = 136. x = 68. So the value od x is 68. That is, the angle C is equal to angle D which is 68o.