Question

In the diagram, lines e and m are parallel to each other and lines p and q are transversals. Use properties of special angles, formed by parallel lines and their transversals, to find the missing angle measures. In the space provided, enter numerical answers only. Note: Figure is not drawn to scale.

e || m; lines p and q are transversals
m∠3 = 65°
m∠15 = 120°

1. m∠7 =
2.m∠4 =
3. m∠6 =
4. m∠1 =
5. m∠16 =
6. m∠18 =
7. m∠21 =
8. m∠10 =
9. m∠11 =
10. m∠12 =

Answer 1

Answer:

Part 1) $m\angle 7=65^o$

Part 2) $m\angle 4=115^o$

Part 3) $m\angle 6=115^o$

Part 4) $m\angle 1=65^o$

Part 5) $m\angle 16=60^o$

Part 6) $m\angle 18=60^o$

Part 7) $m\angle 21=120^o$

Part 8) $m\angle 10=55^o$

Part 9) $m\angle 11=125^o$

Part 10) $m\angle 12=55^o$

Step-by-step explanation:

Part 1) Find the measure of angle 7

we know that

$m\angle 7=m\angle 3$ ----> by corresponding angles

we have

$m\angle 3=65^o$ ----> given

therefore

$m\angle 7=65^o$

Part 2) Find the measure of angle 4

we know that

$m\angle 4+m\angle 3=180^o$ ----> by supplementary angles (form a linear pair)

we have

$m\angle 3=65^o$

substitute

$m\angle 4+65^o=180^o$

$m\angle 4=180^o-65^o=115^o$

Part 3) Find the measure of angle 6

we know that

$m\angle 6=m\angle 4$ ----> by alternate exterior angles

we have

$m\angle 4=115^o$

therefore

$m\angle 6=115^o$

Part 4) Find the measure of angle 1

we know that

$m\angle 1=m\angle 3$ ----> by vertical angles

we have

$m\angle 3=65^o$

therefore

$m\angle 1=65^o$

Part 5) Find the measure of angle 16

we know that

$m\angle 15+m\angle 16=180^o$ ----> by supplementary angles (form a linear pair)

we have

$m\angle 15=120^o$ ---> given

substitute

$120^o+m\angle 16=180^o$

$m\angle 16=180^o-120^o=60^o$

Part 6) Find the measure of angle 18

we know that

$m\angle 18=m\angle 16$ ----> by alternate interior angles

we have

$m\angle 16=60^o$

therefore

$m\angle 18=60^o$

Part 7) Find the measure of angle 21

we know that

$m\angle 21=m\angle 15$ ----> by alternate exterior angles

we have

$m\angle 15=120^o$

therefore

$m\angle 21=120^o$

Part 8) Find the measure of angle 10

step 1

Find the measure of angle 14

we know that

$m\angle 14+m\angle 15=180^o$ ----> by supplementary angles (form a linear pair)

we have

$m\angle 15=120^o$

substitute

$m\angle 14+120^o=180^o$

$m\angle 14=180^o-120^o=60^o$

step 2

we know that

$m\angle 14+m\angle 7+m\angle 12=180^o$ ---> sum of interior angles of a triangle

we have

$m\angle 14=60^o$

$m\angle 7=65^o$

substitute

$60^o+65^o+m\angle 12=180^o$

$m\angle 12=180^o-125^o=55^o$

step 3

Find the measure of angle 10

we know that

$m\angle 10=m\angle 12$ ----> by vertical angles

we have

$m\angle 12=55^o$

therefore

$m\angle 10=55^o$

Part 9) Find the measure of angle 11

we know that

$m\angle 11+m\angle 12=180^o$ ----> by supplementary angles (form a linear pair)

we have

$m\angle 12=55^o$

substitute

$m\angle 11+55^o=180^o$

$m\angle 11=180^o-55^o=125^o$

Part 10) Find the measure of angle 12

see Part 8)

$m\angle 12=55^o$

Answer 2

Answer:

That guy is a absolute mad man