Questions: In the accompanying diagram, AOB is a straight line, m∠AOD=3x-12, and m∠BOD=x. What is the value of x?

In the accompanying diagram, AOB is a straight line, m∠AOD=3x-12, and m∠BOD=x. What is the value of x?
Transcript text: In the accompanying diagram, $\overleftarrow{A O B}$ is a straight line, $\mathrm{m} \angle A O D=3 x-12$, and $m \angle B O D=x$. What is the value of $x$ ?
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Solution

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Solution Steps

Step 1: Set up the equation

Angles AOD and BOD form a straight line, so their measures add up to 180 degrees. Therefore, (3x - 12) + x = 180.

Step 2: Solve for x

Combine like terms: 4x - 12 = 180. Add 12 to both sides: 4x = 192. Divide both sides by 4: x = 48.

Final Answer

x = 48

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