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 $\angle 1={50}^{\circ }$; $\angle 2={90}^{\circ }$; $\angle 3={40}^{\circ }$

$\text{A right-angled triangle is a triangle}\text{where one of the three angles}\text{measures}{90}^{\circ }.$

$\text{Also, sum of interior angles of a}\text{triangle is}{180}^{\circ }.$

$\text{1)}\angle 1={45}^{\circ };\angle 2={45}^{\circ };\angle 3={90}^{\circ }\text{Sum of the angles =}{180}^{\circ }\text{and one angle}\text{measures}{90}^{\circ }.\text{Hence, it is a right}\text{angled triangle.}$

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

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

$\text{4)}\angle 1={50}^{\circ };\angle 2={90}^{\circ };\angle 3={40}^{\circ }\text{Sum of the angles =}{180}^{\circ }\text{and one angle}\text{measures}{90}^{\circ }.\text{Hence, it is a right}\text{angled triangle.}$