Question

in a right angled triangle one of its acute angle is 53° , find the measures of each angle​

Answer 1

The measure of all the angles are :

• The first angle $\sf ( \angle A) = 90 \degree$
• The second angle $\sf (\angle B) = 53 \degree$
• The third angle $\sf (\angle C) = 37 \degree$

Given :–

• In a right angled triangle.
• One of its acute angle = 53°.

To Find :–

• The measure of each angles.

Solution :–

Let,

∆ABC as a right-angled triangle.

It is a right angle so, one angle is 90°.

Let, the $\sf \angle A = 90\degree$

So, the first angle is 90°.

We know that,

Sum of all angles of a triangle is 180°.

I.e.,

$\longmapsto \angle A+ \angle B + \angle C = 180 \degree$

Given that,

• One angle $\sf (\angle B)$ = 53°.

We have to find the other angle $\sf (\angle C)$

$\longmapsto 90 \degree + 53 \degree + \angle C = 180 \degree$

$\longmapsto 143 \degree + \angle C = 180 \degree$

$\longmapsto \angle C = 180 \degree - 143 \degree$

$\longmapsto \angle C = 37 \degree$

So, the second angle is 37°.

Hence,

The measure of the other two angles are 90° and 37°.

The measure of the three angles is 90°, 53° and 37°.

Verification :–

Substitue the values of all the angles in equation (1),

We have,

• $\sf \angle A = 90 \degree$
• $\sf \angle B = 53 \degree$
• $\sf \angle C = 37 \degree$

$\longmapsto \angle A + \angle B + \angle C = 180 \degree$

$\longmapsto 90 \degree + 53 \degree + 37 \degree = 180 \degree$

$\longmapsto 90\degree + \: 90 \degree = 180 \degree$

$\longmapsto 180 \degree = 180 \degree$

Hence Verified !!

Answer 2

Answer:

Angle 1= 90

Angle 2=53

Sum of all angles of a triangle is equal to 180

Therefore

180=90+53+angle 3

Angle 3 =180-143

Therefore

Angle 3 =37 degrees