The measure of the supplement of an angle exceeds three times the measure of the complement of the angle by 12. Find the measure of half of the supplement.

  64.5°

Step-by-step explanation:

The supplement of angle x is 180-x. The complement of the same angle is 90-x, which is 90 less than the supplement.

We can let 'a' represent half the measure of the supplement. Then 2a is the measure of the supplement, and we are given the relation ...

  2a -(3(2a-90)) = 12

  2a -6a +270 = 12 . . . simplify

  258 = 4a . . . . . . . . . . add 4a-12

  a = 64.5

The measure of half the supplement is 64.5 degrees.

Additional comment

Then the supplement of the angle is 129°, and the angle is 51°. Its complement is 39°. 3 times the complement is 117°, which is 12° less than the supplement, as required.

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There are many ways to assign the variable(s) in this problem. Here, we chose one that is pretty direct: the value of the variable answers the question. If you let the variable represent the angle, its complement, or its supplement, then additional work is required to answer the question after the value of the variable is found.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.