Q140 of 158 Page 159

In Fig. 6.46, if y is five times x, find the value of z.

Formula Used/Theory:-

→ Angle sum property

Sum of all angles of triangle is 180°

→ exterior angle is sum of interior opposite angles

If y = 5× x = 5x

By angle sum property

∠R + ∠S + ∠RQS = 180°

60° + y + x = 180°

y + x = 180° -60° = 120°

5x + x = 120°

6x = 120°

x = 20°

y = 5x = 5× 20° = 100°

By exterior angle property

z = 60° + y

z = 60° + 100° = 160°

Result:- the values of x;y;z are 20°;100°;160° resp.

138

Check whether the following measures (in cm) can be the sides of a right-angled triangle or not.

1.5, 3.6, 3.9

139

Height of a pole is 8 m. Find the length of rope tied with its top from a point on the ground at a distance of 6 m from its bottom.

141

The lengths of two sides of an isosceles triangle are 9 cm and 20 cm. What is the perimeter of the triangle? Give reason.

142

Without drawing the triangles write all six pairs of equal measures in each of the following pairs of congruent triangles.

(a) ∆STU ≅ ∆DEF

(b) ∆ABC ≅ ∆LMN

(d) ∆XYZ ≅ ∆MLN