Question

If one angle of a triangle is $\frac{\pi }{4}$ and other angle is ${90}^{\circ }$ then find the third angle in degree measure.

Answer 1

Given that

One angle of a triangle $=\frac{\pi }{4}={45}^{\circ }$

Other angle of triangle $={90}^{\circ }$

Let the third angle be $x^{\circ }$.

We know that the sum of all three angle of any triangle is ${180}^{\circ }$.

Therefore,

${45}^{\circ }+{90}^{\circ }+x^{\circ }={180}^{\circ }$

${135}^{\circ }+x^{\circ }={180}^{\circ }$

$x^{\circ }={180}^{\circ }-{135}^{\circ }$

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

Hence, this is the answer.