Question

if $overline{aob}$ forms a straight angle, $mangle aod=(3x - 12)^{circ}$, and $mangle bod = x^{circ}$. find the angle measures below.

Explanation:

Step1: Use angle - addition postulate

Since $\angle AOB$ is a straight angle, $m\angle AOD + m\angle BOD=180^{\circ}$. So, $(3x - 12)+x = 180$.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side gives $3x+x-12 = 180$, which simplifies to $4x-12 = 180$.

Step3: Add 12 to both sides

$4x-12 + 12=180 + 12$, resulting in $4x=192$.

Step4: Solve for x

Dividing both sides by 4, we get $x=\frac{192}{4}=48$.

Step5: Find $m\angle AOB$

Since $\angle AOB$ is a straight angle, $m\angle AOB = 180^{\circ}$.

Step6: Find $m\angle AOD$

Substitute $x = 48$ into the expression for $m\angle AOD$: $m\angle AOD=(3x - 12)^{\circ}=(3\times48-12)^{\circ}=(144 - 12)^{\circ}=132^{\circ}$.

Step7: Find $m\angle BOD$

$m\angle BOD=x^{\circ}=48^{\circ}$.

Answer:

$x = 48$
$m\angle AOB = 180$
$m\angle AOD = 132$
$m\angle BOD = 48$