Notes

how to find c=
180 is the straight line angle so you take away the degree on the outside from 180. Whatever the answer is is the missing angle on the inside corner. For this one, it would be 180-117 which equals 63. So the inside angle of the bottom right corner (c) equals 63 degrees. It is a straight line angle it is just on a slant.

how to find b=
b is pretty much the same method used. However, for this one the outside angle is 96 degrees. There is a straight line angle (180 degrees) on the bottom so we take away 96 from 180 which now equals 84. Therefore angle b= 84 degrees.

how to find a=
a on the other hand does not have an outside angle therefore it is easier. All we need to do is add all of the sides up and take it away from 360 because our shape is a quadrilateral and therefore the angles sum up to 360.
We already know 112 degrees is the corner so we just have to do 112+63+84. That gives us 259. Then we remove 259 from 360 and we get 101. Therefore angle a is equal to 101 degrees.

Q2:
A quadrilateral has 4 sides that can be equal or unequal. Whatever angle the sides are, they must add up to 360 degrees otherwise it is not a quadrilateral. For this question, it is saying one side measures 84 degrees and another measures 17 degrees. So, we first need to add them together which equals 101 degrees. Now, we take them away from the sum of the quadrilateral (360) and that gives us 259. The last step is to divide it by 2. It is 129.5, and we need an equal number. However, the question gives us 4 different pairs we could use so we will start by using the one. To make the right pair, they must add up to 259 exactly.
The first pair are 90 and 123 degrees. That equals 213, not what we are looking for.
The second pair are 66 and 35 degrees. That equals 101 degrees, again, not what we want.
The third pair are 147 and 112 degrees. They equal 259! Exactly what we want.
The fourth pair are 160 and 87 degrees. They equal 247, not what we want.
The third pair are the correct pair!
Explanation:
A quadrilateral has 4 sides that sum up to 360. The first thing to do is to add 17 onto 84 which gives us 101. Now we know what two sides equal. The next step is to take 101 from the sum of the quadrilateral (360 degrees) and that gives us 259 degrees. From all of the pairs, they must add up to 259 degrees exactly. The first pair don't work because they equal 213, not what we want. The second pair don't work, because they add up to 101 degrees. The fourth pair equal 247, so that means the third pair are correct. That pair equal 259 degrees, so they are correct. Answer=3rd pair (147 and 112)