Question

Find angle AOB: 9x + 41 = 11x - 21

Answer 1

Answer:

∠AOB= 131˚

Step-by-step 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.

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

$2x+21=41$

$2x+21-21=41-21$

$2x=20$

$\frac{2x}{2} =\frac{20}{2}$

$x=10$

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

$AOB=9(10)+41$

$AOB= 90 +41$

$AOB= 131$