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Solution: Exterior angle of a triangle is equal to the sum of interior opposite angles.

(a) In DPQR, ∠PRS = ∠PQR + ∠QPR
So, 115° = x + 50°
x = 115° – 50°
x = 65° Think and Answer
(b) In DABC, ∠BAD = ∠ABC + ∠ACB Can the exterior angle of a
So, 110° = x + 65° triangle be a straight angle?
x = 110° – 65°
x = 45°
Example 4: In a given DABC, ∠ACD = 130° and ∠BAC = ∠ABC. A
Find all the three angles of triangle ABC.
Solution: Given that in DABC, ∠ACD = 130° 130°
And ∠BAC = ∠ABC = x (let) B C D
Since, Exterior angle = Sum of interior opposite angles
∠ACD = ∠BAC + ∠ABC [Exterior angle property of a triangle]

x + x = 130°
2x = 130°

x = 130  = 65°
2
Hence, ∠BAC = ∠ABC = 65°

Angle Sum Property of a Triangle

activity
Take three different colour sheet and put one over other and draw a triangle on the topmost sheet.
Cut all three sheets to get cut out of identical triangles and mark the angles as ∠1, ∠2, ∠3 or ∠A, ∠B and ∠C
as shown in figures.
B B B

2 2 2

1 3 1 3 1 3
A C A C A C
Now, draw a straight line on a paper sheet and place the three interior angles 1, 2, 3 of the three identical triangle
respectively, over the straight line and adjust them to each other without leaving any gap as shown in the figure
below.

3 1
3 1

2
2 1 3 2
Clearly, ∠1 + ∠2 + ∠3 = 180°

175 The Triangle and Its Properties