Question

In the given figure, find the value of $\angle \text{A}+\angle \text{B}+\angle \text{C}+\angle \text{D}+\angle \text{E}+\angle \text{F}$.

• A. 1 right angle
• B. 2 right angles
• C. 3 right angles
• D. 4 right angles

Answer 1

The correct option is D

4 right angles

In triangle ABC, by angle sum property,
$\angle \text{A}+\angle \text{B}+\angle \text{C}={180}^{\circ }$ ...(i)

In triangle CEF, by angle sum property,
$\angle \text{D}+\angle \text{E}+\angle \text{F}={180}^{\circ }$ ...(ii)

Adding (i) and (ii) we get,

$\angle \text{A}+\angle \text{B}+\angle \text{C}+\angle \text{D}+\angle \text{E}+\angle \text{F}={180}^{\circ }+{180}^{\circ }={360}^{\circ }=4\left({90}^{\circ }\right)$

We know that, $4\left({90}^{\circ }\right)$ = 4 right angles

Hence,
$\angle \text{A}+\angle \text{B}+\angle \text{C}+\angle \text{D}+\angle \text{E}+\angle \text{F}$ = 4 right angles