Question

Quadrilateral OPQR is inscribed inside a circle as shown below. What equation would be needed to solve for angle O? What is the measure of angle O? You must show all work and calculations to receive credit.

Answer 1

In an inscribed quadrilateral, opposite angles are supplementary.

Answer 2

Do you know what supplementary angles are?

Answer 3

no I'm sorry

Answer 4

you have two pairs of opposite angles. supplementary means that the angles add up to 180

2x + 2x + 4 = 180

solve for x

Answer 5

Supplementary angles are two angles whose measures add up to 180.

You are looking for the measure of angle O.
Angles O and Q are opposite angles in the quadrilateral.
Since the quadrilateral is inscribed in a circle, then angles O and Q are supplementary.
That means that their measures add up to 180.

m<O + m<Q = 180

The measures of angles O and Q are both expressions in x.
Add the two expressions and set the sum equal to 180.
Then solve for x.

(2x) + (2x + 4) = 180 <--- this is the equation you need
to find the measure of angle O

It simplifies to this:

2x + 2x + 4 = 180

Continue solving the equation until you find what x is.

Once you have a value for x, since m<O = 2x,
use the value of x in 2x to find the measure of angle O.

Answer 6

oh, idk where I got (angle ROP) + (angle RQP) = 180°
(2x)° + (2x + 4)° = 180°
4x = 176
x = 44

angle ROP = (2x)° = 88° from then :/

Answer 7

You are correct.