Question

Two angles form a linear pair. If the measure of the angles are represented by `3x+5` and `x+15`, then what is the value of `x`?

Answer 1

`x=40`

Explanation:

The key realization is that when two angles form a linear pair, they form a straight line, which has a measure of `180^@`.

This means we can set up the following equation:

`color(blue)(3x+5)+color(purple)(x+15)=180`

This equation is saying that the sum of the two measures of the angles (blue and purple expressions) add up to `180` degrees.

In the equation, we can combine our like terms to get

`4x+20=180`

Next, subtract `20` from both sides to get

`4x=160`

Next, we can divide both sides by `4` to get

`x=40`

Hope this helps!