Question

Sum of the three exterior angles of a triangle is ________.

• A. two right angles
• B. three right angles
• C. one right angle
• D. four right angles

Answer 1

Answer: (D)

four right angles

Consider a $△ABC$,

Exterior angle for $\angle A$=$\angle B+\angle C......\left(1\right)$

Exterior angle for $\angle B$=$\angle A+\angle C.........\left(2\right)$

Exterior angle for $\angle C$=$\angle A+\angle B.........\left(3\right)$

Adding equation's $\left(1\right)+\left(2\right)+\left(3\right)$

Exterior angle $A+B+C$=$2(\angle A+\angle B+\angle C)$

Sum of 3 exterior angles of a triangle $=2\left({180}^o\right)={360}^o=4\times {90}^o$

Hence, four right angles.