Question

What is the ratio of the angles in $\Delta ABC$?

• A. $1:1:\sqrt{2}$
• B. $1:1:3$
• C. $1:1:\sqrt{3}$
• D. $1:1:2$

Answer 1

The correct option is D $1:1:2$


From the given figure, we have
$\angle B={90}^{\circ }\text{and}\angle C={45}^{\circ }$

$\angle A+\angle B+\angle C={180}^{\circ }$
[Angle Sum Property]
$\Rightarrow \angle A+\angle B+{45}^{\circ }={180}^{\circ }$
$\Rightarrow \angle A+{90}^{\circ }+{45}^{\circ }={180}^{\circ }\Rightarrow \angle A={180}^{\circ }-{135}^{\circ }\Rightarrow \angle A={45}^{\circ }$

$\angle A:\angle B:\angle C={45}^{\circ }:{45}^{\circ }:{90}^{\circ }={45}^{\circ }:{45}^{\circ }:(45\times 2{)}^{\circ }$

$\therefore$ Dividing throughout by ${45}^{\circ }$, we get
1 : 1 : 2.