Question

Find the value of x and y in the given figures.​

Answer 1

Answer:

X=45° each

Y= 90° hope you got it

Answer 2

Concepts used :

Vertically opposite angles : This property says that any line segments, rays or lines that intersect each other are always equal in the measurements of their angles. We can also conclude that any line that forms a shape of the letter 'X' can be considered as the vertically opposite angles.

Interior angle sum property : This property is only applicable for all the types of triangles. This property says that, if we add all the measurements of the angle in a triangle, then their sum should add up to 180°. If this condition is not applicable for the triangle, then it cannot be considered as a triangle.

Solution

Value of ∠y :

As we know that the vertically opposite angles are equal. So, the value of the ∠y is same as it's vertically opposite angle.

${\sf \dashrightarrow \angle{y} = {90}^{\circ}}$

Now, let's find the value of the angle x.

Value of ∠x :

As we know that all the angles of a triangle measures 180° together.

${\sf \dashrightarrow \angle{A} + \angle{B} + \angle{C} = {180}^{\circ}}$

${\sf \dashrightarrow 90 + x + x = {180}^{\circ}}$

${\sf \dashrightarrow 90 + 2x = {180}^{\circ}}$

${\sf \dashrightarrow 2x = 180 - 90}$

${\sf \dashrightarrow 2x = 90}$

${\sf \dashrightarrow x = \dfrac{90}{2}}$

${\sf \dashrightarrow x = {45}^{\circ}}$

Hence, the values of x and y are 45° and 90° respectively.