Two friends are sharing one half of a pizza that is divided into three pieces, as shown in the figure.

Question

Two friends are sharing one half of a pizza that is divided into three pieces, as shown in the figure.

If m∠AOB = (6x − 5)° and m∠BOD = (9x + 17)°, what is the value of x?

1. 117.8 
2. 62.2 
3. 11.2 
4. 7.3

Answer 1

Angles AOB and BOD are supplementary, meaning that together they form a straight line, AOD, or a straight angle.

A straight line measures 180 degrees, so

m∠AOB + m∠BOD = 180º.

Substituing the expressions given for the angle measurements, and dropping the degree marks temporarily for the sake of simplicity, we have

( 6x - 5 ) + ( 9x + 17) = 180

Gathering up like terms,

15x + 12 = 180

Subtracting 12 from both sides,

15x = 168

Dividing both sides by the coefficient of x,

x = 11.2

and that is answer choice 3.

To check:

6x - 5 = 6*11.2 - 5 = 62.2

9x + 17 = 9*11.2 + 17 = 117.8

62.2 + 117.8 = 180

Answer 2

What can we say about these two angles, ∠AOB & ∠BOD?

I will give you a hint: We can say what degree measure add up to. And we can use that to set up an equation to solve for x.