Question

In an isosceles triangle ABC, if segment BA is congruent to segment BC and m∠BCA = 48°, what is m∠CXA?

A) 132°
B) 96°
C) 66°
D) 24°

Answer 1

In an isosceles triangle ABC, if segment BA is congruent to segment BC and m∠BCA = 48°, the measure of angle CBA is 66°.

Step-by-step explanation:

In an isosceles triangle ABC, if segment BA is congruent to segment BC and m∠BCA = 48°, the triangle is symmetrical and angles CAB and CBA are congruent. Since the sum of the angles in a triangle is 180°, the measure of angle CAB and CBA can be calculated as follows:

1. CAB + CBA + BCA = 180° (sum of angles in a triangle)
2. m∠CBA + m∠CBA + 48° = 180° (replace CAB and BCA with CBA since they are congruent)
3. 2(m∠CBA) + 48° = 180°
4. 2(m∠CBA) = 180° - 48°
5. 2(m∠CBA) = 132°
6. m∠CBA = 132° / 2
7. m∠CBA = 66°

Therefore, m∠CBA is 66°. So, the answer is option C) 66°.