Question

Which correctly describes how to determine the measure of angle 1?Which correctly describes how to determine the measure of angle 1?

A.The 105° angle and angle 2 are alternate exterior angles so angle 2 must measure 105°. Angles 1 and 2 are supplementary angles so angle 1 must measure 75°.
B.The 105° angle and angle 2 are corresponding angles so angle 2 must measure 105°. Angles 1 and 2 are supplementary angles so angle 1 must measure 75°.
C.The 105° angle and angle 2 are alternate exterior angles so angle 2 must measure 75°. Angles 1 and 2 are supplementary angles so angle 1 must measure 105°.
D.The 105° angle and angle 2 are corresponding angles so angle 2 must measure 75°. Angles 1 and 2 are supplementary angles so angle 1 must measure 105°.

Answer 1

A

Explanation:

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Answer 2

Option A

The
`105\°` angle and angle 2 are alternate exterior angles so angle 2 must measure
`105\°`. Angles 1 and 2 are supplementary angles so angle 1 must measure
`75\°`

Explanation:

we know that

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

and

`m<1+m<2=180\°` ----> by supplementary angles

Substitute the value of angle 2 and find the value of angle 1

`m<1+105\°=180\°`

`m<1=180\°-105\°=75\°`

therefore

the answer is the option A