Question

In the diagram above, suppose m*ANGLE*6=115°. Explain how to find the measures of each of the other seven
numbered angles.
(please check aswell)​

Answer 1

Answer:

see the explanation

Step-by-step explanation:

step 1

Find the measure of angle 2

we know that

$m\angle 2=m\angle 6$ -----> by corresponding angles

so

$m\angle 2=115^o$

step 2

Find the measure of angle 3

we know that

$m\angle 3=m\angle 2$ -----> by vertical angles

so

$m\angle 3=115^o$

step 3

Find the measure of angle 7

we know that

$m\angle 7=m\angle 6$ -----> by vertical angles

so

$m\angle 7=115^o$

step 4

Find the measure of angle 4

we know that

$m\angle 4+m\angle 6=180^o$ -----> by consecutive interior angles (supplementary angles)

so

$m\angle 4+115^o=180^o$

$m\angle 4=65^o$

step 5

Find the measure of angle 1

we know that

$m\angle 1=m\angle 4$ -----> by vertical angles

so

$m\angle 1=65^o$

step 6

Find the measure of angle 5

we know that

$m\angle 5=m\angle 4$ -----> by alternate interior angles

so

$m\angle 5=65^o$

step 6

Find the measure of angle 8

we know that

$m\angle 8=m\angle 5$ -----> by vertical angles

so

$m\angle 8=65^o$