Question

The degree measure of an angle and its supplement are consecutive odd integers. Find the measure of each angle.

Answer 1

Answer:

89

91

Step-by-step explanation:

Supplementary means the pair of angles that have this relationship add up to 180 degrees.

If you assume n is odd, then the very next odd number is n+2.

Example 5 is odd and the next odd number after 5 is 7. This fits the pattern of n and n+2 when n=5.

So we are given the degree measurement of an angle and it's supplement are consecutive odd integers.

So let's pretend the supplement of A is B. This means A+B=180.

We are also given A and B are consecutive odd integers, so this means we are going to let A=n and B=n+2.

Let's put this into our equation for A+B=180:

(n)+(n+2)=180

n  + n+2 =180

2n     +2 =180

Subtract 2 on both sides:

2n          =178

Divide both sides by 2:

 n           =178/2

Simplify right hand side:

 n           =89

If n=89, then n+2=89+2=91.

Does 89+91=180? Yep.

Are 89 and 91 consecutive odd numbers?  Yep.  

Here are some consecutive numbers including those: 89,90,91

Yes 91 is the next odd number after 89.

Answer 2

Answer:

89° , 91°

Step-by-step explanation:

Let x and x+2 be the two consecutive odd numbers

x + x + 2 = 180

2x = 178

x = 89

x + 2 = 91