The supplement of an angle is three times the complement of the angle. Find the measure of 1/2 supplement of the complement

Question

my teacher worded this problem really weird and left a  of typos and I can't figure out how to do this help please

Answer 1

Find 1/2  supplement of the complement.

First determine the complement. You did this  when you obtained 45 degrees.

Next, determine the supplement of the complement. Again, you found this when you obtain 180-45 = 135 degrees.

Finally, 1/2 (supplement of complement) = 1/2 x 135 = 67.5 degrees.

 

You did really well in explaining the steps- just the slip up on the last line. (Hey! No one is perfect. I have made slip ups too).

 

Note:  'of' does not mean multiplication as is the case in fractions.

Answer 2

Complementary angles add up to 90 degrees.  Supplementary angles add up to 180 degrees.   First we need to find the angle.

 

Let the reference angle = x

Let the supplement of angle = (180 - x)

Let the complement of angle = (90 - x)

 

 

Now we set the equations for the complementary and supplementary angle to solve for x.

 

180 - x = 3(90 - x)

 

180 - x = 270 - 3x

 

 

Add x on both sides of equation.

 

180 = 270 - 2x

 

 

Subtract 270 on both sides of equation.

 

-90 = -2x

 

 

Divide both sides of equation by -2.

 

45 = x

 

 

The reference angle is 45 degrees.  Now we substitute this reference angle into the other two angles.

 

Complement = 90 - 45 = 45 degrees

Supplement = 180 - 45 = 135 degrees

 

 

Finally, we find the last part of the problem.

 

(1/2) * (135) * (45) = 3037.50 degrees