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Therefore, ∠BAC = ∠ACE ......(i) A E

(Alternate interior angles)
∠ABC = ∠ECD .....(ii)
(Corresponding angles) B C D
Adding (i) and (ii), we get

∠BAC + ∠ABC = ∠ACE + ∠ECD ….(iii)
But ∠ACE + ∠ECD = ∠ACD ….(iv)

(Sum of adjacent angles)
Therefore, from (iii) and (iv), we get
∠BAC + ∠ABC = ∠ACD
Or ∠ACD = ∠BAC + ∠ABC
Hence, the measure of the exterior angle is equal to the sum of the measurement of the interior
opposite angles.

At every vertex of a triangle there are one interior and two exterior angles.
A

Exterior
Note: Interior angle
angle
B C D
Exterior
angle

Example 2: In the given DABC, ∠ACD is the exterior angle. Find: A
(a) the measure of ∠ACD. 58°

(b) third angle of the triangle.
Solution: Given, ∠ABC = 60°, ∠BAC = 58° 60° x
B C D
(a) We know that exterior angle of a triangle is equal to the sum of the interior opposite
angles. In ΔABC,
∠ACD = ∠ABC + ∠BAC
So, ∠ACD = 60° + 58° = 118°
(b) ∠ACB + ∠ACD = 180° (Linear pair of angles)

∠ACB + 118° = 180°
∠ACB = 180° – 118°
So, ∠ACB = 62°
Example 3: Find the value of x in the following triangles:

(a) P (b) D
A
50° 110°

115°
x
Q R S x 65°
B C

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