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In the diagram below of isosceles triangle ABC, AB is congruent to CB and angle bisectors AD, BF and CE are drawn and intersect at x.

If the measure of angle BAC=50°, find the measure of AXC

In the diagram below of isosceles triangle ABC AB is congruent to CB and angle bisectors AD BF and CE are drawn and intersect at xIf the measure of angle BAC50 class=

Respuesta :

Answer:

[tex]130^{\circ}[/tex]

Step-by-step explanation:

We know that in an triangle , angles opposite to equal sides are equal .

Given : [tex]AB=CB[/tex]

So, [tex]\angle A=\angle C[/tex] .

We get [tex]\angle C=\angle A=50^{\circ}[/tex]

Since AD bisects [tex]\angle A[/tex] , [tex]\angle XAC=\frac{1}{2}\angle A=\frac{1}{2}(50^{\circ})=25^{\circ}[/tex]

Also, as CE bisects [tex]\angle C[/tex] , [tex]\angle XCA=\frac{1}{2}\angle C=\frac{1}{2}(50^{\circ})=25^{\circ}[/tex]

We will use angle sum property which states that in [tex]\Delta XAC[/tex] ,

[tex]\angle XAC+\angle XCA+\angle AXC=180^{\circ}[/tex]

[tex]25^{\circ}+25^{\circ}+\angle AXC=180^{\circ}\\50^{\circ}+\angle AXC=180^{\circ}\\\angle AXC=180^{\circ}-50^{\circ}\\=130^{\circ}[/tex]