Question

In this figure a || b Find the measure of each angle using either of the given angle measures. Identify the reason for each answer

∠1
∠2
∠3
∠4
∠5
∠6

Answer 1

`m<1=99\°`

`m<2=81\°`

`m<3=86\°`

`m<4=86\°`

`m<5=86\°`

`m<6=94\°`

Explanation:

Part 1) Find the measure of angle 1

we know that

`m<1+81\°=180\°` -----> by supplementary angles

`m<1=180\°-81\°=99\°`

Part 2) Find the measure of angle 2

we know that

`m<2=81\°` -----> by alternate exterior angles

Part 3) Find the measure of angle 3

we know that

`m<3=86\°` -----> by vertical angles

Part 4) Find the measure of angle 4

we know that

`m<4=86\°` ------> by corresponding angles

Part 5) Find the measure of angle 5

we know that

`m<5=m<4` -----> by vertical angles

so

`m<5=86\°`

Part 6) Find the measure of angle 6

we know that

`m<5+m<6=180\°` -----> by supplementary angles

we have

`m<5=86\°`

substitute

`86\°+m<6=180\°`

`m<6=180\°-86\°=94\°`