Find the values of x and y in Fig. 6.37
Solution:
Given, the figure represents a triangle.
We have to find the values of x and y.
Consider a triangle TQS,
Angle sum property of a triangle states that the sum of all three interior angles of a triangle is always equal to 180 degrees.
∠T + ∠Q + ∠S = 180°
50° + 30° + ∠1 = 180°
80° + ∠1 = 180°
∠1 = 180° - 80°
∠1 = 100°
We know that the sum of a linear pair of angles is equal to 180 degrees.
So, ∠S = 180°
∠1 + ∠2 = 180°
100° + ∠2 = 180°
∠2 = 180° - 100°
∠2 = 80°
Consider a triangle TSR,
By angle sum property,
∠T + ∠S + ∠R = 180°
∠2 + x + 45° = 180°
80° + x + 45 = 180°
x + 125° = 180°
x = 180° - 125°
x = 55°
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite interior angles of the triangle.
By exterior angle property,
∠y = ∠Q + ∠R
∠y = 30° + 45°
∠y = 75°
Therefore, the values of x and y are 55° and 75°.
✦ 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 125
Find the values of x and y in Fig. 6.37
Summary:
The values of x and y in Fig. 6.37 are 55° and 75°.
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