Question
Two friends are sharing one half of a pizza that is divided into three pieces, as shown in the figure.
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
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
Answers
GPT 3.5
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.
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.