Isosceles triangle ABC contains angle bisectors segment BF, segment AD, and segment CE that intersect at X.
triangle ABC with diagonals BF, AD, and EC that intersect at point X
If segment BA is congruent to segment BC and m∠BCA = 44°, what is m∠CXA?
136°
132°
68°
44°
m∠CXA is 132°.
Since triangle ABC is isosceles, we know that segment BA is congruent to segment BC. This means that m∠BAC = m∠BCA. Since m∠BCA is 44°, m∠BAC is also 44°.
Since segment BF is an angle bisector of ∠BAC, we know that m∠FAC = m∠BAC = 44°.
Now, considering triangle AXC, we know that the sum of the angles in a triangle is 180°. Therefore, m∠CXA = 180° - (m∠FAC + m∠BAC) = 180° - (44° + 44°) = 180° - 88° = 92°.
Therefore, m∠CXA is 92°.