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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 136^o, what is the value of x?

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 = x^o and angle C = x^o

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 nonadjacent interior angles. In this problem, we get angle ABD = angle D + angle C. Given angle ABD is 136^o, then x + x = 136. 2x = 136. x = 68. So, the value of x is 68. That is, the angle C is equal to angle D which is 68^o.