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 = 46°, what is m∠CXA?

Answer:The measure of angle CXA is 134°Step-by-step explanation:* Lets explain how to solve the problem - Triangle ABC is an isosceles triangle where AB = BC∵ AB = BC- The base angles in the isosceles triangle are congruent∴ m∠BAC = m∠BCA∵ m∠ BCA = 46° ⇒ given∴ m∠ BAC = 46°- The sum of the measures of the interior angles in any triangle is 180°∵ m∠BAC + m∠BCA + m∠ABC = 180°- Substitute the values of angle BAC and BCA in the equation above∴ 46 + 46 + m∠ABC = 180∴ 92 + m∠ABC = 180 - Subtract 92 from both sides∴ m∠ABC = 88°- BF , AD , CE are bisectors segments of angles B , A , C and they are   intersected at point X∵ CE bisects ∠BCA∵ X ∈ CE∴ m∠XCA = 1/2 m∠BCA∴ m∠XCA = 1/2 (46) = 23°∵ AD bisects ∠BAC∵ X ∈ AD∴ m∠XAC = 1/2 m∠BAC∴ m∠XAC = 1/2 (46) = 23°- In Δ AXC∵ m∠XAC = 23° ⇒ proved∵ m∠XCA = 23° ⇒ proved∵ m∠CXA + m∠XAC + m∠XCA = 180° ⇒ interior angles of ΔSubstitute the values of angles XAC and XCA∴ m∠AXC + 23 + 23 = 180∴ m∠CXA + 46 = 180- Subtract 46 from both sides∴ m∠CXA = 134°* The measure of angle CXA is 134°