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

Question

Circle O has diameter A D and radii B O and C O. Angle A O B is adjacent to angle B O C. Angle B O C is adjacent to angle C O D.

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

117.8
62.2
11.2
7.3

Answer 1

To solve for x, we can set up an equation using the fact that the sum of the angle measures in a triangle is 180 degrees.

Since AOB and BOC are adjacent angles formed by the same pair of rays, we can write:
m∠AOB + m∠BOC + m∠AOC = 180 degrees.

Substituting in the given angle measures, we have:
(6x - 5) + (9x + 17) + (6x - 5) = 180.

Combining like terms, we get:
21x + 7 = 180.

Subtracting 7 from both sides:
21x = 173.

Dividing both sides by 21:
x = 8.24.

Therefore, the value of x is 8.24, which is not one of the given answer choices.