Find the measure of ∠1.
If you were writing a proof, you'd use the angle addition postulate and the definition of supplementary angles.
∠1 = 69°
Find the measure of ∠2.
The Exterior Angle Theorem says that an exterior angle equals the sum of the two remote interior angles. Our remote interior angles are 28° and ∠2.
∠2 = 83°
Find the measure of ∠3.
Vertical angles or supplementary angles. Whichever you feel like.
∠3 = 111°
Find the measure of ∠4 if it is equal to twice the measure of ∠5.
Remember that ∠3 = 111°.
∠4 = 46°
What is the measure of ∠5 if it equals half the measure of ∠4?
Even doing geometry, algebra has once again come back to haunt us.
∠5 = 23°
Find the measure of ∠6.
This isn't supplementary information.
∠6 = 39°
Find the measure of ∠7.
Do exterior angles deserve their own theorem? We think so.
∠7 = 102°
Make it rain.