Question

$\text{Select the possible interior opposite angles}\text{of the triangle with an exterior angle}\text{of}{150}^{\circ }.$

• A. ${50}^{\circ }$, ${100}^{\circ }$
• B. ${120}^{\circ }$, ${75}^{\circ }$
• C. ${75}^{\circ }$, ${30}^{\circ }$
• D. ${40}^{\circ }$, ${120}^{\circ }$

Answer 1

The correct option is A ${50}^{\circ }$, ${100}^{\circ }$

An exterior angle of a triangle is equal to the sum of its opposite interior angles.

$\text{Given: Exterior angle =}{150}^o$

$\text{So, the sum of the opposite}\text{interior angles should be}{150}^o.$

${100}^o+{50}^o={150}^o$
${120}^o+{75}^o={195}^o$
${75}^o+{30}^o={105}^o$
${40}^o+{120}^o={160}^o$

$\text{So, the correct answer is}{50}^{\circ },{100}^{\circ }.$