Question

If G is the incenter of △ABC, find m∠ABC and m∠CAG.

A) m∠ABC = m∠CAG
B) m∠ABC = 2m∠CAG
C) m∠ABC = 3m∠CAG
D) m∠ABC = 4m∠CAG

Answer 1

To find the measures of angles ∠ABC and ∠CAG, we need to recall that the incenter of a triangle is equidistant from the three sides of the triangle. Therefore, m∠ABC = m∠CAG.

Step-by-step explanation:

To find the measures of angles ∠ABC and ∠CAG, we first need to recall a property of the incenter of a triangle. The incenter is the point of concurrency of the angle bisectors of the triangle. This means that the incenter is equidistant from the three sides of the triangle.

Since G is the incenter of △ABC, it is equidistant from AB, BC, and CA. This means that the distance from G to AB is equal to the distance from G to BC, and the distance from G to BC is equal to the distance from G to CA.

Therefore, we have AG = GB and BG = GC. This implies that ∠ABC and ∠CAG are congruent. Hence, m∠ABC = m∠CAG. The correct option is A) m∠ABC = m∠CAG.