Question

ABCD is a quadrilateral inscribed in a circle:

Circle O is shown with a quadrilateral ABCD inscribed inside it. Angle A is labeled x plus 16. Angle B is labeled x degrees. Angle C is labeled 6x minus 4. Angle D is labeled 2x plus 16.

What equation can be used to solve for angle D?

(2x + 16) + (6x - 4) = 90
(x + 16) - (x) = 90
(x + 16) + (2x + 16) = 180
(2x + 16) + (x) = 180

Answer 1

I think D..

Answer 2

@Directrix

Answer 3

Theorem: Opposite angles of a quadrilateral inscribed in a circle are supplementary.

Answer 4

Meaning they add up to 180 degrees..

Answer 5

Correct. Here's a reference on that theorem:

http://www.geom.uiuc.edu/~dwiggins/conj47.html

Answer 6

So my answer is Correct..

Answer 7

*Correct..?

Answer 8

Angles B and D are opposite angles. So, yes, this equation is correct.

(2x + 16) + (x) = 180

Answer 9

Okay, thanks.

Answer 10

You are welcome.