Exterior Angle Theorem
The exterior angle theorem says that an exterior angle of a triangle equals the sum of the two interior angles not adjacent to it. It follows directly from the fact that a triangle totals 180 degrees and a straight line does too.
(∠x) is the exterior angle.
(∠x + 92 = 180º) (linear pair of angles)
(∠x =:180-92 = 88º)
Applying the exterior angle theorem, we get, (∠y + 41 = 88)
(∠y = 88-41= 47º)
Exercises for Exterior Angle Theorem
- What is the value of (p) in the triangle?
- Find (m∠YDC).
- Find (x) in the given triangle and then find (m∠ABD).
- (color{blue}{60^{circ }})
- (color{blue}{140^{circ }})
- (color{blue}{x=5, m∠ABD = 100^{circ }})
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