Question

two friends are sharing one half of a pizza that is divided into three pieces, as shown in the figure. if ( mangle aob=(2x - 4)^{circ} ) and ( mangle bod=(14x + 12)^{circ} ), what is the value of x? 1.30 10.75 17.40 162.50

Explanation:

Step1: Determine the relationship between the angles

Since \( \angle AOB\) and \( \angle BOD\) are supplementary (they form a straight - line, and the measure of a straight - line angle is \(180^{\circ}\)), we have the equation \((2x - 4)+(14x + 12)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2x+14x-4 + 12=180\), which simplifies to \(16x+8 = 180\).

Step3: Solve for \(x\)

Subtract \(8\) from both sides: \(16x=180 - 8=172\). Then divide both sides by \(16\): \(x=\frac{172}{16}=10.75\).

Answer:

\(10.75\)