Question

aob forms a straight angle, m∠aod=(3x - 12)°, and m∠bod = x°, find the angle measures below

Explanation:

Step1: Use straight - angle property

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

Adding 12 to both sides of the equation $4x-12 = 180$ gives $4x=180 + 12$, so $4x=192$.

Step4: Solve for x

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

Step5: Find $\angle AOD$

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

Step6: Find $\angle BOD$

Since $m\angle BOD=x^{\circ}$, and $x = 48$, then $m\angle BOD = 48^{\circ}$. And $m\angle AOB = 180^{\circ}$ (by the definition of a straight angle).

Answer:

$m\angle AOB = 180^{\circ}$
$m\angle AOD = 132^{\circ}$
$m\angle BOD = 48^{\circ}$