Question

Given △ABC with AB ≅ AC and m∠B=39°, find m∠C.
a) 51°
b) 102°
c) 39°

Answer 1

In isosceles triangle ►ABC, given that AB ≅ AC and m∠B is 39°, the measure of angle C, m∠C, is also 39° because the base angles of an isosceles triangle are congruent.

Step-by-step explanation:

The question involves finding the measure of an angle in a triangle, specifically in an isosceles triangle ►ABC where AB ≅ AC. Given that m∠B = 39°, we can determine m∠C using the fact that the base angles in an isosceles triangle are congruent. Since AB is congruent to AC, it follows that ∠B is congruent to ∠C. Therefore, m∠C must also be 39°.

Step-by-step explanation:

1. Identify that ►ABC is isosceles with AB ≅ AC.
2. Recall that in an isosceles triangle, the base angles are congruent.
3. Since m∠B is given as 39°, m∠C must also be 39° because it is the base angle congruent to ∠B.