Question

In a right-angled triangle, if one acute angle is ${45}^o$then the third angle is _________.

Answer 1

Firstly let a triangle $△ABC$.

According to the angle sum property of a triangle, the sum of all interior angles of a triangle is ${180}^o$.

In $△ABC$, $\angle A+\angle B+\angle C={180}^0$.

And $\angle B={90}^o$ and $\angle C={45}^o$.

So, put the value of given angles, $\angle A+{90}^o+{45}^o={180}^o$.

$$\begin{gathered} \angle A={180}^o-{135}^o={45}^0 \\ \angle A={45}^o \end{gathered}$$

Hence, In a right-angled triangle, if one acute angle is ${45}^o$then the third angle is ${45}^o$.