Angle Word Problem: HELP!

Question

Two angles are complementary. The sum of the measures of the larger angle and three times the measure of the smaller angle is 114 degrees. What is the measure of each angle?

Answer 1

If two angles are complementary then  if larger angle is x and smaller is y ;  x+y=90

as it is given

larger angle + 3 times smaller angle =114

               x+3y   = 114

            x+y+y+y=114

             90 + 2y = 114    ( as x+y= 90)

                     2y = 114 - 90

                     2y = 24

                       y= 24/2 =12

 

smaller angle y =12^o

and larger angle x = 90- y = 90 - 12= 78^o

Answer 2

Justine,

 

 Let's name the two angles "x" and "y". (I'm going to leave out "degrees" until the end) So,

 

 x: smaller angle

 y: larger angle

 

By definition, two angles are complementary if they add up to 90 degrees. So then, we know that

 

 x+y=90.   It also says the SUM (going to add) of the measures of the LARGER ANGLE (meaning y) and THREE TIMES THE MEASURE OF THE SMALLER ANGLE (meaning 3 times x, or just 3x)  IS (meaning equal to) 114 degrees. Translating this sentence to an equation gives us

 

 y+3x=114.    Now, we have two equations:

 

 

 

 1) x+y=90

 2) y+3x=114.      You can solve this system by any method. I'll use substitution. Solving the first equation for y gives us

 

 y=90-x. Plugging that value for y into equation 2 yields

 

 

 (90-x)+3x=114--> 2x=24-->x=12

 

 Plugging that value for x into our equation for y above, we get

 

 y=90-12--> y=78. So we have x=12 degrees and y=78 degrees. Are these correct? Let's check by plugging them in to equations 1 and 2 at the top:

 

12+78=90?-->  90=90  yes!

 

78+3(12)=114? -->78+36=114? --> 114=114 yes!

 

Hope this helps.

Answer 3

Let a and b be the two angles, with a being the larger angle.  Since the two angles are complementary, they add up to 90^o:

 

     a + b = 90^o, so a = 90^o-b

 

The sum of the measures of the larger angle and three times the measure of the smaller angle is 114^o:

 

     a + 3b = 114^o

 

Substitute 90-b in place of a:

 

     90^o - b + 3b = 114^o

     2b = 24^o

     b= 12^o

 

     a = 90^o - b = 90^o - 12o = 78^o