Question

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Quadrilateral OPQR is inscribed in circle N, as shown below. Which of the following could be used to calculate the measure of ∠ROP?

Circle N is shown with a quadrilateral OPQR inscribed inside it. Angle O is labeled x plus 16. Angle P is not labeled. Angle Q is labeled 6x minus 4. Angle R is labeled 2x plus 16.

(6x − 4)° + (2x + 16)° = 360°
(x + 16)° + (6x − 4)° = 360°
(6x − 4)° + (2x + 16)° = 180°
(x + 16)° + (6x − 4)° = 180°

Answer 1

In an inscribed quadrilateral, opposite angles are supplementary.

Answer 2

ok

Answer 3

but im confused

Answer 4

Look for two angles that are
1) opposite angles
2) that you are given an expression for their measures.

Can you name them?

Answer 5

Q and O ?

Answer 6

Correct.
Since opposite angles are supplementary, if you add their measures, the sum equals 180.
That gives you an equation is only x, which you can then solve.
Once you know the value of x, you can plug it in the expression for angle O and find its measure.

Look in the 4 choices.
Which equation is the sum of the measures of the opposite angles you have expressions for and then set to equal 180?

Answer 7

the second and the fourth

Answer 8

well only the 4th

Answer 9

tnx now i understand

Answer 10

Correct. Only the 4th choice.

Answer 11

ur da best :D