Question

Which sets of values can be the measures of the exterior angles of a triangle?

• A. $120°,110°,130°$
• B. $35°,103°,122°$
• C. $123°,87°,220°$
• D. $120°,120°,120°$
• E. $123°,157°,90°$

Answer 1

Answer: (A), (D)

$120°,120°,120°$

Explanation for correct options:

We know that sum of exterior angles of a triangle is ${360}^{\circ }$.

Option (A) : $120°+110°+130°={360}^{\circ }$
Option (D) : $120°+120°+120°={360}^{\circ }$

Thus, $120°,110°,130°$ and $120°,120°,120°$ are the possible measures of the exterior angles of a triangle.

Explanation for incorrect options:

Option (B) : $35°+103°+122°={260}^{\circ }$
Option (C) : $123°+87°+220°={430}^{\circ }$
Option (E) : $123°+157°+90°={370}^{\circ }$

Hence, options (A) and (D) are correct.