Question

In a right-angled triangle, one of the acute angles measures 53°. Find the measure of each angle of the triangle.

Answer 1

Finding the values of all the angles of a triangle:

Given data:

1. The given triangle is a right angled triangle.
2. One of the acute angle measures 53°

Let us assume the triangle to be $△ABC$

As we know the triangle is right angled,

$\therefore \angle C=90°$

and one angle measures 53°,

$\therefore \angle A=53°$

We know that the sum of all angles of a triangle is 180°

The sum of all angles of a triangle is equal to 180°

So we can write,

$$\begin{gathered} \angle A+\angle B+\angle C=180° \\ 53°+\angle B+90°=180° \\ 143°+\angle B=180° \\ \angle B=180°-143° \\ \angle B=37° \end{gathered}$$

Hence, measures of each angle of triangle are $\mathbf{\angle }\mathbf{A}\mathbf{}\mathbf{=}\mathbf{}\mathbf{53}\mathbf{°}\mathbf{,}\mathbf{}\mathbf{\angle }\mathbf{B}\mathbf{}\mathbf{=}\mathbf{}\mathbf{37}\mathbf{°}\mathbf{,}\mathbf{}\mathbf{\angle }\mathbf{C}\mathbf{}\mathbf{=}\mathbf{}\mathbf{90}\mathbf{°}$