Question

In $△$ABC, the exterior angle to A measures ${110}^{\circ }$ and $\angle$C measures ${30}^{\circ }$. What is the measure of $\angle$B?

• A. ${70}^{\circ }$
• B. ${80}^{\circ }$
• C. ${90}^{\circ }$
• D. ${100}^{\circ }$

Answer 1

The correct option is B

${80}^{\circ }$

The interior and the exterior angle at A make a linear pair. Therefore, their sum would be ${180}^{\circ }$.
Hence, interior $\angle$A = ${180}^{\circ }$ – ${110}^{\circ }$ = ${70}^{\circ }$.

Since the sum of all interior angles of a triangle is equal to ${180}^{\circ }$,
therefore, $\angle$B = ${180}^{\circ }$ - ( $\angle$A + $\angle$C)
or, $\angle$B = ${180}^{\circ }$ - ( ${70}^{\circ }$ + ${30}^{\circ }$) = ${80}^{\circ }$