Question

What is the measure of 8?

120°
90°
60°
180°
_____________________________


What type of angles are 1 and 5?



vertical
supplementary
corresponding
complementary

Answer 1

The measure of
`\angle 8` is 60°

`\angle 1` and
`\angle 5` are corresponding angles.

Explanation:

Given that,
`m\angle 2= 120\°`

In the given diagram,
`\angle 2` and
`\angle 6` are corresponding angles and their measures are same.

So,
`m\angle 6= 120\°`

Now,
`\angle 6` and
`\angle 8` are pair of linear angles.

That means......

`m\angle 6+m\angle 8= 180`°

`\Rightarrow 120\°+m\angle 8=180\°\\ \\ \Rightarrow m\angle 8= 180\°-120\°\\ \\ \Rightarrow m\angle 8=60\°`

So, the measure of
`\angle 8` is 60°

The type of angles for
`\angle 1` and
`\angle 5` is corresponding.

Answer 2

< 8 = 60

<1 and <5 are corresponding angles

Explanation:

<2 = <3 vertical angles

<3 = <6 alternate interior angles

<6 + <8 = 180 supplementary angles

120 + <8 = 180

Subtract 120 from side

120-120 + <8 = 180-120

< 8 = 60

<1 and <5 are corresponding angles

Corresponding angles occupy the same relative position at each intersection.