Question

Solve for x and find the value of the bolded angle.

Answer 1

75°

Explanation:

The two given angle measures (defined in terms of x) are alternate interior angles. Therefore, the are congruent. This means that their angles measures are equal. We can express this with an equation, and solve for x:

`9x + 3 = 8x + 11`

↓ subtracting
`8x` from both sides

`x + 3 = 11`

↓ subtracting 3 from both sides

`\boxed{x = 8}`

Now, we can plug this into the bolded angle's definition:

`9x + 3`

↓ plugging in
`x=8`

`9(8) + 3`

↓ executing the multiplication

`72 + 3`

↓ executing the addition

`\boxed{75\°}`