Question

In a right-angled triangle, one of the acute angles measures ${53}^{\circ }$. Find the measure of each angle of the triangle.

Answer 1

Consider $ABC$ as a right-angled triangle with $\angle C={90}^{\circ }$

We know that the sum of all the angles in a triangle is ${180}^{\circ }$.

So we can write it as

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

We can write it as

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

By substituting the values

$\angle A+\angle B={180}^{\circ }-{90}^{\circ }$

By subtraction

$\angle A+\angle B={90}^{\circ }$

Let us consider $\angle A={53}^{\circ }$

By substituting the value of $\angle A$ in $\angle A+\angle B={90}^{\circ }$

We get

${53}^{\circ }+\angle B={90}^{\circ }$

On further calculation

$\angle B={90}^{\circ }-{53}^{\circ }$

By subtraction

$\angle B={37}^{\circ }$

Therefore, $\angle A={53}^{\circ },\angle {37}^{\circ }$ and $\angle C={90}^{\circ }$.