I need putting this word sentence into a mathematical sentence.
Find the measure of an angle if the sum of the measures of its complement and supplement is 162o.
(90-x) + (180-x) = 162
solve for x
Call the angle A, its complement C, its supplement S.
A + C = 90
A + S = 180
C + S = 162.
Three equation and three unkmnowns.
I would solve equation 3 for C and substitute that into equation 1. Then solve 1 and 2 simultaneously. Post your work if you get stuck.
I've solved for X before but for some reason I'm stuck on this one. How do I solve for X here?
To translate the word sentence into a mathematical sentence, let's break it down:
Statement: Find the measure of an angle.
Translation: Let's assume the measure of the angle is x.
Statement: The sum of the measures of its complement and supplement is 162 degrees.
Translation: The complement of an angle is 90 degrees minus the angle itself, and the supplement of an angle is 180 degrees minus the angle itself. So, we can set up the equation:
complement + supplement = 162
To express the complement and supplement in terms of x:
complement = 90 - x
supplement = 180 - x
Substituting the values into the equation:
90 - x + 180 - x = 162
Simplifying the equation:
270 - 2x = 162
Now, we can solve for x:
270 - 162 = 2x
108 = 2x
x = 54
Therefore, the measure of the angle is 54 degrees.