Math word problem I need help with please?

Question

Two angels are complementary. The sum of the measure of the first angle and half the second angel is 87 degrees.

1. what is the measure of the smaller angel?

2. what is the measure of the other angel?

Answer 1

You can think of mathematics as a different language.  The trick to mastering word problems is learning how to translate from written phrases (sentences) to mathematical phrases (equations).  Below, I'll post the sentences in your problem and then their mathematical translations.

Definitions:

x = first angle

y = second angle

"Two angles are complementary"

x + y = 90°

"The sum of the measure of the first angle and half the second angel is 87 degrees"

x + y/2 = 87°

So now you have a system of 2 equations and exactly 2 unknowns (x & y), which means the system can be solved:

1) x + y = 90°

2) x + y/2 = 87°

Subtract (2) from (1):

(x+y) - (x + y/2) = 90° - 87°

y/2 = 3°

y = 6°

Now substitute this value for y into either (1) or (2):

x + 6° = 90°

x = 84°

Answer 2

Smaller is 6 degrees, larger is 84.

Answer 3

complementary means that the sum of the angles is equal to 90 degrees..thus we can derive our mathematical expression from the problem..

let x --- the first angle

    y---- the second angle  

              

sol:

x+ y = 90 ------- 1st equation

x+y/2 = 87 ------ 2nd equation.

then solve this either by elimination or substitution...but for me I will use the substitution method..to do this, just choose one out of the two equation to be rewrite in the form y=mx+b...

I will choose equation 2..It will then become...

x+ y = 90 ------- 1st equation

x = 87 - y/2 ------ 2nd equation.

then substitute the value of x from equation 2 to equation 1

87- y/2 + y = 90  (combine like terms)

          y-y/2=90-87

          y-y/2=3   (multiply both sides by 2..to eliminate the number 2

                                         from y)

          2y-y=6

              y=6  

then substitute the value of y either from the two equations to find the value of x...I will choose equation 1

x+y=90

x+6=90  (combine like terms)

     x=90-6

     x=84  

ANSWER:

x=84 degrees  ----- other angle

y=6 degrees  ------ smaller angle

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