Question

if angle 1 and angle 2 form a linear pair. if m<1=5x+9 and m<2=3x+11, find the measure of both angles

Answer 1

Answer:
`m\angle 1=109\°\\m\angle 2=71\°`

Explanation:

It is important to remember the definition of "Linear pair angles".

By definitiion "Linear pair angles" are two angles which are adjacents and supplementary.

Based on this, we know that the angles
`\angle1` and
`\angle2` are supplementary, which means that they add up to 180 degrees.

So, knowing that:

`m\angle 1=5x+9\\m\angle 2=3x+11`

We can write the following expression and solve for "x":

`(5x+9)+(3x+11)=180\\\\8x=180-20\\\\x=(160)/(8)\\\\x=20`

Therefore, substituting, we get that the measures of the angles
`\angle1` and
`\angle2` are:

`m\angle 1=5(20)+9=109\°\\\\\\m\angle 2=3(20)+11=71\°`