The measure of one angle is 3 degrees more than 1/2 the measure of its supplement

Question

The measure of one angle is 3 degrees more than 1/2 the measure of its supplement

Answer 1

Let's decode the question. Because it says that one angle is related to another, we know there are two angles. Give their measures names (preferably one letter names), say a and b. The relationship between the angles is "one angle" (a) "is" (=) "three more" (3 +) "than one half the measure of [the other angle]" ( (1/2)*b ).

OR: a = 3 + (1/2) b

We also know that the angles are supplements, because the angle we are calling b is a's supplement. Supplementary angles are those whose sum is 180 degrees. (I remember the difference between Supplementary and Complementary angles, angles that add to 90 degrees by "Complementary angles complement each other because together they are always right")

Knowing that the two angles are supplementary gives us the second equation necessary to solve the problem: a + b = 180

Now you can solve for b in terms of a (or the reverse): b = 180 - a, and substitute this into the first equation:

a = 3 + (1/2)(180 - a)

Solving this should be straight forward. My first step would be to multiply through by 2 to eliminate the fraction in the second term on the right hand side.

2a = 6 + 180 - a

Group like terms: (add a to both sides of the equation and add 180 + 3)

3a = 186 ==> a = 62, b = 180 - 62 = 118

Check: (1/2) b = 118 / 2 = 59. a = 3 + 59 = 62