In Fig. 6.46, if y is five times x, find the value of z.
Solution:
Given, SRQ is a triangle.
Angle y is five times the angle x.
We have to find the value of z.
According to the question,
y = 5x
Angle sum property of a triangle states that the sum of all three interior angles of a triangle is always equal to 180 degrees.
∠R + ∠S + ∠Q = 180°
60° + y + x = 180°
60° + 5x + x = 180°
6x = 180° - 60°
6x = 120°
x = 120°/6
x = 20°
Now, y = 5(20°) = 100°
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,
z = 60° + y
z = 60° + 100°
Therefore, z = 160°
✦ Try This: Check whether the following measures (in cm) can be the sides of a right-angled triangle or not. 2.3, 2.6, 4.9
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6
NCERT Exemplar Class 7 Maths Chapter 6 Problem 140
In Fig. 6.46, if y is five times x, find the value of z.
Summary:
In Fig. 6.46, if y is five times x, the value of z is 160°.
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