Question

If a triangle has angle measures of `4x+5, 7x,` and `7x-5`, what is the value of `x`?

Answer 1

`x=10`

Explanation:

The sum of the internal angle in a triangle is `180^o`

So `(4xcancel(+5))+(7xcancel(-5))+(7x)=180`

`18x=180`

`x=10`

Answer 2

#x=10

Explanation:

To solve this problem we require to know that.

`color(blue)"Sum of the 3 angles in a triangle" = 180^@`

The angles here are given as algebraic expressions, but the principle is the same. That is sum them and equate to 180.

`(color(red)(4x+5))+(color(red)(7x))+(color(red)(7x-5))=180`

now collect like terms.

`color(blue)(4x)cancel(+5)+color(blue)(7x)+color(blue)(7x)cancel(-5)=180`

`rArr18x=180`

divide both sides by 18 to solve for x

`(cancel(18)^1 x)/cancel(18)^1=cancel(180)^(10)/cancel(18)^1rArrx=10`

The size of the 3 angles are therefore.

`4x+5=(4xx10)+5=45^@`

`7x=7xx10=70^@`

`7x-5=(7xx10)-5=70-5=65^@`

and `45^@+70^@+65^@=180^@`