Given:
[tex]\angle ABC=(4x+2)^o,\angle ACB=(2x-9)^o,\angle XAC=(5x+13)^o[/tex]
[tex]We\text{ know that }\angle BAC\text{ and }\angle XAC\text{ are supplementary angles.}[/tex]
The sum of the supplementary angles =180 degrees.
[tex]\angle BAC+\angle XAC=180^o[/tex]
[tex]\text{ Substitute }\angle XAC=(5x+13)^o\text{ in the equation.}[/tex]
[tex]\angle BAC+(5x+13)^o=180^o[/tex]
[tex]\angle BAC=180^o-\mleft(5x+13\mright)^o[/tex]
We know that the sum of all three angles of the triangle is 180 degrees.
[tex]\angle ABC+\angle ACB+\angle BAC=180^o[/tex]
[tex]\text{ Substitute }\angle ABC=(4x+2)^o,\angle ACB=(2x-9)^o,\angle BAC=180^o-(5x+13)^o\text{.}[/tex]
[tex](4x+2)^o+(2x-9)^o+180^o-(5x+13)^o=180^o[/tex]
[tex](4x+2)^o+(2x-9)^o-(5x+13)^o=180^o-+180^o[/tex]
[tex](4x+2)^o+(2x-9)^o-(5x+13)^o=0[/tex]
[tex]4x+2+2x-9-5x-13=0[/tex]
Adding like terms that have the same variable with the same powers.
[tex]4x+2x-5x+2-9-13=0[/tex]
[tex]x-20=0[/tex][tex]x=20[/tex]
Hence the value of x is 20.
