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How do I solve for x? Would my answer be 27?

How Do I Solve For X Would My Answer Be 27 class=

Sagot :

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.

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