Question

11. In the given figure, if ABCD is a square, the
value of x is
(a) 45°
(b) 60°
(c) 70°
(d) 36°
​

Answer 1

The correct option regarding the angle x is (b) 60°.

Given:

A square ABCD.

To Find:

The angle x.

Solution:

To find the angle x we will follow the following steps:

As we know,

Opposite angles are equal

∠ DOC = ∠ AOB = 105°

∠ BOC = ∠ AOD = x

Now,

The sum of all the angles at the intersection point O is 360°.

So,

∠ 105° + 105° + ∠ BOC + ∠ AOD = 360°

210° + 2x = 360°

2x = 360° - 210°

$2x = 150$

$x = \frac{150}{2} = 75$

In triangle BOC:

∠ BOC = 45° = OCX (Because diagonals bisect the right angle(90°) of the square)

Also,

In triangle COX:

The sum of all three angles of the triangle is 180°.

So,

∠ COX + ∠ CXO + ∠ OCX = 180°

$75 + ∠ CXO + 45 = 180$

$∠ CXO + 120 = 180$

$∠ CXO = 180 - 120 = 60$

Henceforth, the correct option regarding the angle x is (b) 60°.

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