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

ANSWERS:
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.

Evaluating the measure of angle 3, you find it to be (2·7+6)° = 20°. Vertical angles are equal; angles created from a right angle are complementary; two right angles add to 180°, so are supplementary. Using these relationships, you can determine the applicable answers to be ...

• The measure of angle 6 is 20°.

• The measure of angle 5 is 70°.

• Angles 1 and 4 are supplementary. (Only because two 90° angles are supplementary. In general, vertical angles are not supplementary.)

calculista calculista · Answer 2 · 2019-01-29T17:37:04+01:00

Answer:

The measure of angle [tex]6[/tex] is [tex]20\°[/tex]

The measure of angle [tex]5[/tex] is [tex]70\°[/tex]

Angles [tex]1[/tex] and [tex]4[/tex] are supplementary

Step-by-step explanation:

we have that

[tex]m<3=(2x+6)\°[/tex]

so

For [tex]x=7[/tex]

[tex]m<3=(2(7)+6)\°=20\°[/tex]

Statements

Verify each statement

case A) The measure of angle [tex]6[/tex] is [tex]20\°[/tex]

The statement is True

we know that

[tex]m<6=m<3[/tex] ------> by vertical angles

we have that

[tex]m<3=20\°[/tex]

so

[tex]m<6=20\°[/tex]

case B) The measure of angle [tex]5[/tex] is [tex]70\°[/tex]

The statement is True

we know that

[tex]m<5+m<6=90\°[/tex] ------> by complementary angles

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

[tex]20\°+m<5=90\°[/tex]

[tex]m<5=90\°-20\°=70\°[/tex]

case C) The measure of angle [tex]2[/tex] is [tex]80\°[/tex]

The statement is False

we know that

[tex]m<2=m<5[/tex] ------> by vertical angles

we have that

[tex]m<5=70\°[/tex]

so

[tex]m<2=70\°[/tex]

case D) Angles [tex]2[/tex] and [tex]5[/tex] are complementary

The statement is False

we know that

[tex]m<2=m<5[/tex] ------> by vertical angles

so

Angles [tex]2[/tex] and [tex]5[/tex] are vertical angles and its sum is not equal to [tex]90\°[/tex]

case E) Angles [tex]5[/tex] and [tex]6[/tex] are supplementary

The statement is False

we know that

[tex]m<5+m<6=90\°[/tex] ------> by complementary angles

so

Angles [tex]5[/tex] and [tex]6[/tex] are complementary angles

case F) Angles [tex]1[/tex] and [tex]4[/tex] are supplementary

The statement is True

we know that

[tex]m<1=m<4[/tex] ------> by vertical angles

[tex]m<1+m<4=180\°[/tex] ------> by supplementary angles

Because

[tex]m<1=90\°[/tex] and [tex]m<4=90\°[/tex]

so

Angles [tex]1[/tex] and [tex]4[/tex] are vertical angles and are supplementary angles