Question

Which of the following can be classified as right angled triangles?

• A. $\angle 1={45}^{\circ }$; $\angle 2={45}^{\circ }$; $\angle 3={90}^{\circ }$
• B. $\angle 1={25}^{\circ }$; $\angle 2={45}^{\circ }$; $\angle 3={110}^{\circ }$
• C. $\angle 1={50}^{\circ }$; $\angle 2={45}^{\circ }$; $\angle 3={90}^{\circ }$
• D. $\angle 1={50}^{\circ }$; $\angle 2={90}^{\circ }$; $\angle 3={40}^{\circ }$

Answer 1

Answer: (A), (D)

The correct options are
A $\angle 1={45}^{\circ }$; $\angle 2={45}^{\circ }$; $\angle 3={90}^{\circ }$
D $\angle 1={50}^{\circ }$; $\angle 2={90}^{\circ }$; $\angle 3={40}^{\circ }$

A right angled triangle is a triangle where one of the three angles measures ${90}^{\circ }$.
Also sum of interior angles of a triangle = ${180}^{\circ }$

In $\angle 1={25}^{\circ }$; $\angle 2={45}^{\circ }$; $\angle 3={110}^{\circ }$: No angle measures ${90}^{\circ }$, hence it is not a right angled triangle.

In $\angle 1={50}^{\circ }$; $\angle 2={45}^{\circ }$; $\angle 3={90}^{\circ }$: Sum of angles = ${185}^{\circ }$. Hence, such a triangle is not possible.

$\angle 1={45}^{\circ }$; $\angle 2={45}^{\circ }$; $\angle 3={90}^{\circ }$ and
$\angle 1={50}^{\circ }$; $\angle 2={90}^{\circ }$; $\angle 3={40}^{\circ }$
qualify as right angled triangles.