Isosceles triangle ABC contains angle bisectors segment BF, segment AD, and segment CE that intersect at X.

If segment BA is congruent to segment BC and m∠BCA = 48°, what is m∠CXA?

132°
96°
66°
24°

Option A:

m∠CXA=132°

Step-by-step explanation:

Triangle ABC is an isosceles triangle.

In isosceles triangle, angles opposite to congruent sides are congruent.

⇒ m∠BCA = m∠BAC = 48°

Segment AD bisect angle m∠BAC.

m∠BAX = m∠XAC = 24°

Segment CE  bisect angle  m∠BCA.

m∠BCX = m∠XCA = 24°

The sum of the interior angles of triangle = 180°

In triangle AXC,

m∠XCA + m∠XAC + m∠CXA = 180°

24° + 24° + m∠CXA = 180°

48° + m∠CXA = 180°

m∠CXA = 180° – 48°

m∠CXA = 132°

Option A is the correct answer.

step-by-step explanation: