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 Δ
Substitute the values of angles XAC and XCA
∴ m∠AXC + 23 + 23 = 180
∴ m∠CXA + 46 = 180
- Subtract 46 from both sides
∴ m∠CXA = 134°
* <em>The measure of angle CXA is 134°</em>
