Question

Find angle AOB:

9x + 41 = 11x - 21

Answer 1

∠AOB= 131˚

Explanation:

Recall the Vertical Angles Theorem, which states that when two lines intersect, vertical angles are congruent. With this, ∠AOB ≅ ∠COD

To find the value of x, make the equation:

`11x+ 21=9x+41`

Solve it out.

`11x +21-9x=9x+41-9x`

`2x+21=41`

`2x+21-21=41-21`

`2x=20`

`(2x)/(2) =(20)/(2)`

`x=10`

Now that we know the value of x, insert the value of x for the equation of ∠AOB to find its measure.

`AOB=9(10)+41`

`AOB= 90 +41`

`AOB= 131`