Geometry: Finding Angle Measures

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1. D

The supplementary angle to the 112° angle is 78°.  So, the last angle in the quadrilateral must be 112°.

2. E

$\eqalign{3x+99&=180\\3x&=81\\x&=27\\\\18 + 99 + y &= 180\\117+y&=180\\y&=63\\x+y&=\\27+63&=90}$$

3. E

The top triangle equals 180.  So:

$$\eqalign{45+18+a&=180\\63+a&=180\\a&=117\\\\\text{The top angle of the side triangle is supplementary to 117}\\117 + b &= 180\\b&=63\\\\\text{The angles of the side triangle add up to 180}\\x + 2x + 63&=180\\3x+ 63&=180\\3x&=117\\x&=39}$$

4. 60

The average of the angles of all of the angles in triangles is always 60.  The angles of a triangle always add up to 180.  180 divided by 3 is always 60.  Remember, averages are averages -- even if the individual numbers are different, the averages will be the same.