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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