Question

I honestly don't know how I got these answers and I have a test over it coming soon. Please explain how to find the measure of these angles.

Answer 1

Okay so a couple of things to know to best solve this problem
1) all angles in a triangle add to 180
2) a straight line the angles above it equal 180 and the angles below it add to 180
3) vertical angles are equal (vertical angles are angles that make an X the opposite angles are called vertical angles)

Answer 2

Things to remember:  

-a triangle's angles all add up to equal 180 degrees
-two angles that share a side, that create a straight line also add up to 180 deg.

So for the following:
angle 1: the triangle beside it is missing an angle. add 68+36=104, now 180-104=76. That angle shares a side with angle 1, so you can do 180-76=104.

angle 4: shares a side with 70 and 65. Together, they all three make a straight line. So add 70+65=135. Then 180-135=45.

angle 3: shares a side with 70 and angle 4(you found to be 45). Again, they make a straight line, so add 70+45=115. Then 180-115=65.

angle 2: is in the same triangle as angle 3(you found to be 65). The missing angle in that same triangle shares a side with 36. So 180-36=144, now 180-144 to find the missing angle=36. Now add 36+65=101. Now 180-101=79

angle 5: you know angle 4=45. So to find the other missing angle in that same triangle, do 180-118=62. Now add 62+45=107. Finally, 180-107=73.

Hope this helps.