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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 136o, 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 = 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 nonadjacent 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 of x is 68.
That is, the angle C is equal to angle D which is 68o.