Question

two friends are sharing one half of a pizza that is divided into three pieces, as shown in the figure. if (mangle aob=(6x - 5)^{circ}) and (mangle bod=(9x + 17)^{circ}), what is the value of x? 117.8 62.2 11.2 7.3

Explanation:

Step1: Note angle relationship

Since one - half of a circle is 180°, and \(\angle AOB\) and \(\angle BOD\) together make up one - half of the circle, we have \(m\angle AOB + m\angle BOD=180^{\circ}\).
So, \((6x - 5)+(9x + 17)=180\).

Step2: Combine like - terms

Combine the \(x\) terms and the constant terms: \((6x+9x)+(- 5 + 17)=180\), which simplifies to \(15x+12 = 180\).

Step3: Isolate the variable term

Subtract 12 from both sides of the equation: \(15x=180 - 12\), so \(15x=168\).

Step4: Solve for \(x\)

Divide both sides by 15: \(x=\frac{168}{15}=11.2\).

Answer:

11.2