Question

if ( mangle aob=(2x - 4)^{circ} ) and ( mangle bod=(14x + 12)^{circ} ), what is the value of ( x )?

Explanation:

Step1: Set up the equation

Since \( \angle AOB\) and \( \angle BOD\) are right angles (assuming they form a straight - line or some other relation where their sum is \(180^{\circ}\), but if they are adjacent angles at the center of a circle and form a semicircle, \(m\angle AOB + m\angle BOD=180^{\circ}\)). So, \((2x - 4)+(14x + 12)=180\).

Step2: Simplify the left - hand side

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

Step3: Isolate the term with \(x\)

Subtract \(8\) from both sides: \(16x=180 - 8\), so \(16x=172\).

Step4: Solve for \(x\)

Divide both sides by \(16\): \(x=\frac{172}{16}=10.75\).

Answer:

\(10.75\)