Find the measure of all the missing angles

a = 68°, b = 112°, c = 68°

Step-by-step explanation:

There is an angle on your drawing that is referenced with an arc and a tic mark drawn through the arc.  Let's call this angle "x".

On the left side of the graph, 112° and x are congruent (equal) because they are Vertical Angles.  x = 112°

Notice that angle x is also on the right side of the graph.

a and x form a Linear Pair so they are supplementary angles (their sum equals 180°).  a + x = 180   ⇒   a + 112 = 180   ⇒   a = 68°

b and x are congruent because they are Vertical Angles.  So, b = 112°

a and c are congruent because they are Vertical Angles.  So, c = 68°

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