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 $x$ ?

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Answer 1 · 2018-07-06T01:09:18

$x=40$

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!

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