Table of Contents
- Exterior Angles – Example
- What’s Next?
In the previous segment, we learnt about the Exterior and interior angles of a triangle and its property. In this segment, we will solve an interesting problem based on exterior angles.
Exterior Angles – Example
Q. In the given figure, find the sum of the three exterior angles.
Figure 1
Solution:
The three exterior angles are ∠EAB, ∠ACD, and ∠FBC.
According to the exterior angle property of a triangle, the exterior angle is equal to the sum of the interior opposite angles.
∴ ∠EAB = ∠ACB + ∠ABC … (1)
∠ACD = ∠BAC + ∠ABC… (2)
∠FBC = ∠BAC + ∠ACB … (3)
Adding statements (1), (2), and (3),
∠EAB + ∠ACD + ∠FBC = ∠ACB + ∠ABC + ∠BAC + ∠ABC + ∠BAC + ∠ACB
∴ ∠EAB + ∠ACD + ∠FBC = 2 (∠ACB + ∠ABC + ∠BAC) … (4)
∠ACB, ∠ABC and ∠BAC are the interior angles of Δ ABC and the sum of the interior angles of a
triangle is 180°.
∴ ∠ACB + ∠ABC + ∠BAC = 180°
Substituting the above equation in equation (4),
