Question

Line a is  parallel to b, m<6=85, and m<3=2x. Find m<1

Answer 1

Angle 3 = 2x

Angle 3 = Angle 1 Reason: Vertically opposite angles are equal.

Angle 1 = Angle 3 = 2x

Angle 1 = 2x

Angle 3 + Angle 6 = 180 Sum of opposite interior angles = 180

Angle 3 + 85 = 180

Angle 3 = 180 -85 = 95

Recall Angle 1 = Angle 3

Angle 1 = 95 degrees.

Answer 2

Angle 3 and 6 are consecutive interior angles so their sum is equal to 180

`85 + 2x =180`
since 1 and 3 are vertical angles they have the same measure. The goal is to find angle 3 to find angle 1.

`85 + 2x =180`
We take our equation add solve it.

`2x = 180-85 \\ 2x=95 \\ x=47.5`
Now we know x so we can plug that back into 2x to figure out the value of angle 3. 2(47.5) = 95 That is the measure of angle 3. Since 1 and 3 are vertical angles they have the same measure. 1=95