I need help with geometry angles?

Question

If supplement of an angle has a measure 78 less than the measure of the ange, what are the measures of the angles?

Answer 1

Emily, the key is to turn this geometry problem into a 2-equation / 2-unknown algebra problem.

A = Angle

S = Supplement

 

A + S = 180 degrees (definition of supplementary angles)

S = A - 78 (The supplement (S) has a measure (=) of the angle (A) less 78)

 

Substituting the 2nd equation into the first

A + A - 78 = 180

+78              +78

2A = 258

/2       /2

A = 129

S = 129 - 78 = 51

Check:

A + S = 129 + 51 = 180