SOLUTION: how would I write an algebraic expression for this? "two angles form a linear pair. the measure of one angle is 51 degrees more than 1/2 the measure of the other angle"

Question 996669: how would I write an algebraic expression for this? "two angles form a linear pair. the measure of one angle is 51 degrees more than 1/2 the measure of the other angle"
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x = the measure of one angle
y = the measure of the other angle.

the measure of one angle is 51 degrees more than 1/2 the measure of the other angle.
x = 1/2 * y + 51

-----

since they are a linear pair, the sum of their angles must be equal to 180 degrees.

you get x + y = 180
since x = 1/2 * y + 51, you can replace x with 1/2 * y + 51 to get:
1/2 * y + 51 + y = 180
subtract 51 from both sides of this equation to get:
1/2 * y + y = 180 - 51 = 129
combine like terms to get:
3/2 * y = 129
multiply both sides of this equation by 2/3 to get:
y = 129 * 2 / 3 = 86.

you are given that x = 1/2 * y + 51
this makes x = 43 + 51 = 94
94 + 86 = 180
looks good.

x = 94 degrees
y = 86 degrees

since you were only asked to write the algebraic equation, you can stop at -----. the rest just tells you how to solve for each of those angles based on the information given.

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