In the figure, BEST is a rhombus, Then the value of y - x is
(a) 40°
(b) 50°
(c) 20°
(d) 10°

Solution:

Given, BEST is a rhombus.

We have to find the value of y - x.

In a rhombus, opposite sides are parallel and the opposite angles are equal.

All the sides of a rhombus are equal in length, and the diagonals bisect each other at right angles.

Considering TS || BE with BS as transversal,

We know that the alternate interior angles are equal.

∠ESB = ∠TSB = 40°

Since the diagonals bisect each other at right angles,

∠y = 90°

Considering triangle TSO,

∠OTS + ∠OST = ∠EOS

x + 40° = 90°

x = 90° - 40°

x = 50°

Now, y - x = 90° - 50° = 40°

Therefore, the required value is 40°.

✦ Try This: Which of the following can be the measure of exterior angle of a regular polygon? (a) 22°, (b) 13°, (c) 45°, (d) 17°

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 41

Summary:

In the figure, BEST is a rhombus, Then the value of y - x is 40°.

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