Question

A triangle has ∠1 and ∠2 as remote interior angles with respect to exterior angle ∠3. Given that m∠1 = 50 and m∠2 = 70, Alicia reasoned that m∠3 must be 60. Is Alicia correct? If not, explain Alicia's error.

Answer 1

No, 60 is the third interior angle's mesure, not the exterior ∠3.

Explanation:

Say that ∠1=∠A=50 and ∠2=∠B=70. The remote interior angles are the angles that are not touvhing the exterior angle. So ∠3 would be the the exterior angle to ∠C. ∠C=60 as the sum of the interior angles is 180.

The exterior angle is the angle formed by extending one of the triangle's sides. A straight line has the angle 180, so∠3=180-∠C=180-60=120.