Question

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

Answer 1

Given:

`\angle ABC=(4x+2)^o,\angle ACB=(2x-9)^o,\angle XAC=(5x+13)^o`

`We\text{ know that }\angle BAC\text{ and }\angle XAC\text{ are supplementary angles.}`

The sum of the supplementary angles =180 degrees.

`\angle BAC+\angle XAC=180^o`

`\text{ Substitute }\angle XAC=(5x+13)^o\text{ in the equation.}`

`\angle BAC+(5x+13)^o=180^o`

`\angle BAC=180^o-\mleft(5x+13\mright)^o`

We know that the sum of all three angles of the triangle is 180 degrees.

`\angle ABC+\angle ACB+\angle BAC=180^o`

`\text{ Substitute }\angle ABC=(4x+2)^o,\angle ACB=(2x-9)^o,\angle BAC=180^o-(5x+13)^o\text{.}`

`(4x+2)^o+(2x-9)^o+180^o-(5x+13)^o=180^o`

`(4x+2)^o+(2x-9)^o-(5x+13)^o=180^o-+180^o`

`(4x+2)^o+(2x-9)^o-(5x+13)^o=0`

`4x+2+2x-9-5x-13=0`

Adding like terms that have the same variable with the same powers.

`4x+2x-5x+2-9-13=0`

`x-20=0`
`x=20`

Hence the value of x is 20.