The triangle ΔXAC formed by the angle bisectors is an isosceles triangle
The measure of m∠CXA is the option;
136°
Reason:
The given parameters are;
ΔABC = An isosceles triangle
BF, AD, and CE = Angle bisectors, intersect at X
m∠BCA = 44°
m∠XCF = m∠XCD Angles formed by angle bisector CE
We have;
m∠BCA = 44° = m∠XCF + m∠XCD; by angle addition Postulate
∴ 44° = m∠XCF + m∠XCF; by substitution property of equality
44° = 2 × m∠XCF
- [tex]m \angle XCF= \dfrac{44^{\circ}}{2} = 22^{\circ}[/tex]
m∠EAF = m∠XAF + m∠XAE
m∠XAF = m∠XAE; Angles formed by angle bisector AD
∴ m∠EAF = m∠XAF + m∠XAF
m∠EAF = 2 × m∠XAF
m∠EAF = 44°; by base angles of isosceles triangle
- [tex]m \angle XAF= \dfrac{44^{\circ}}{2} = 22^{\circ}[/tex]
m∠CXA + m∠XCF + m∠XAF = 180° Angle sum property of a triangle
m∠CXA = 180° - (m∠XCF + m∠XAF )
Which gives;
m∠CXA = 180° - (22° + 22°) = 136°
- The measure of m∠CXA = 136°
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