Question

If the measure of angle 3 is equal to (2x + 6)° and x = 7, which statements are true? Check all that apply.

The measure of angle 6 is 20°.
The measure of angle 5 is 70°.
The measure of angle 2 is 80°. Angles 2 and 5 are complementary.
Angles 5 and 6 are supplementary.
Angles 1 and 4 are supplementary.

Answer 1

The measure of angle
`6` is
`20\°`

The measure of angle
`5` is
`70\°`

Angles
`1` and
`4` are supplementary

Explanation:

we have that

`m<3=(2x+6)\°`

so

For
`x=7`

`m<3=(2(7)+6)\°=20\°`

Statements

Verify each statement

see the attached figure to better understand the problem

case A) The measure of angle
`6` is
`20\°`

The statement is True

we know that

`m<6=m<3` ------> by vertical angles

we have that

`m<3=20\°`

so

`m<6=20\°`

case B) The measure of angle
`5` is
`70\°`

The statement is True

we know that

`m<5+m<6=90\°` ------> by complementary angles

Substitute the value of m<6 and solve for m>5

`20\°+m<5=90\°`

`m<5=90\°-20\°=70\°`

case C) The measure of angle
`2` is
`80\°`

The statement is False

we know that

`m<2=m<5` ------> by vertical angles

we have that

`m<5=70\°`

so

`m<2=70\°`

case D) Angles
`2` and
`5` are complementary

The statement is False

we know that

`m<2=m<5` ------> by vertical angles

so

Angles
`2` and
`5` are vertical angles and its sum is not equal to
`90\°`

case E) Angles
`5` and
`6` are supplementary

The statement is False

we know that

`m<5+m<6=90\°` ------> by complementary angles

so

Angles
`5` and
`6` are complementary angles

case F) Angles
`1` and
`4` are supplementary

The statement is True

we know that

`m<1=m<4` ------> by vertical angles

`m<1+m<4=180\°` ------> by supplementary angles

Because

`m<1=90\°` and
`m<4=90\°`

so

Angles
`1` and
`4` are vertical angles and are supplementary angles