In Fig. 6.31(ii), find the values of a, b and c.
Solution:
Given, the figure represents a triangle ABC.
We have to determine the values of a, b and c.
Angle sum property of a triangle states that the sum of all three interior angles of a triangle is always equal to 180 degrees.
Considering triangle PQS,
By angle sum property,
∠QPS + ∠PQS + ∠PSQ = 180°
55° + 60° + a = 180°
a + 115° = 180°
a = 180° - 115°
a = 65°
Considering triangle PQR,
∠P + ∠Q + ∠R = 180°
55° + c + 60 + 40 = 180°
55° + 100° + c = 180°
155° + b = 180°
c = 180° - 155°
c = 25°
Considering triangle PSR,
∠PSR + ∠SPR + ∠PRS = 180°
c + b + 40° = 180°
25° + b + 40° = 180°
65° + b = 180°
b = 180° - 65°
b = 115°
Therefore, the values of a, b and c are 65°, 115° and 25°.
✦ Try This: Find the value of x.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6
NCERT Exemplar Class 7 Maths Chapter 6 Problem 109 (ii)
In Fig. 6.31(ii), find the values of a, b and c.
Summary:
In Fig. 6.31(ii), the values of a, b and c are 65°, 115° and 25°.
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