Question

1. solve for x
2. angles aod and dob are supplementary angles. what is the value of x?

Explanation:

Step1: Set up equation for first - problem

Since vertical angles are equal, we have $4(x + 1)=88$.

Step2: Expand the left - hand side

$4x+4 = 88$.

Step3: Subtract 4 from both sides

$4x=88 - 4$, so $4x=84$.

Step4: Divide both sides by 4

$x=\frac{84}{4}=21$.

Step5: Set up equation for second - problem

Since angles AOD and DOB are supplementary, $116 + 2x=180$.

Step6: Subtract 116 from both sides

$2x=180 - 116$, so $2x = 64$.

Step7: Divide both sides by 2

$x=\frac{64}{2}=32$.

Answer:

For the first problem, $x = 21$.
For the second problem, $x = 32$.