the measure of the angle is nine times greater than its supplement, what is the supplement

Question

I need help with this problem i do not understand it it is due at 12:00 pm and i need help my math teacher is not available.. 

Answer 1

Let x be the unknown angle.  Supplementary angles add to 180^o, so the supplementary angle of x is 180^o-x.

• the measure of the angle (x)
• is (=)
• nine times greater than its supplement (9*(180^o-x))

 

x = 9(180^o-x)

x = 1620^o - 9x

10x = 1620^o

x = 162^o

 

The measure of the supplement is 180^o - x = 180^o - 162^o = 18^o

Answer 2

Supplementary angles are two angles that add up to 180 degrees.

 

Let the angle = x

Let the supplement = 180 - x

 

 

We can set the equation.

 

x = 9(180 - x)

 

x = 1620 - 9x

 

 

Add 9x on both sides of the equation.

 

10x = 1620

 

 

Divide 10 on both sides of the equation.

 

x = 162

 

 

The angle is 162.

 

 

The supplement is    180 - 162 = 18

 

 

 

 

Answer 3

As with many "word problems", the hardest part is translating the words into math.  Let's start by coming up with math symbols and equations for each phrase in the problem.

 

"The measure of the angle":

    Let's call the angle "X" in this problem.

 

"is nine times greater than its supplement":

    Let's call the supplement "S", if the angle X is 9 times greater than S, then X = 9S

 

"what is the supplement":

    What is the definition of a supplement of an angle?  A supplement is what you would need to add to an angle to get to 180°, or written in math symbols, S = (180° - X)

 

I have 2 points to make here:

    1. What information can you solve for using the 2 equations I provided above?

    2. Remember, the question is asking you ultimately to find the supplement.

 

Does this help?

Answer 4

Hey there,

Lets first understand the concept of supplementary angles - Two Angles are Supplementary when they add up to 180 degrees.

 

Lets say the supplementary angle is 'x'. So the angle would be 9*x. The equation can be stated as -

x + 9*x = 180 ( because they are supplementary angles)

10*x = 180.

Therefore, x = 180/10.

x = 18 degrees

 

The supplementary angle is 18 degrees.