Question

I Really need help! I don’t understand this! Will give 100 points!

Quadrilateral OPQR is inscribed inside a circle as shown below. Which pairs, or pairs, of angles are supplementary.


Answer choices:

All 4 angles = 180

Can not be determined, there is not enough information given


All pairs combinations shown are supplementary

Answer 1

Answer:

• ∠P and ∠R; ∠O and ∠Q

Step-by-step explanation:

• Opposite angles of the cyclic quadrilateral are supplementary.

Angles P and R are opposite to each other, the arcs intercepted by these two angles make a full circle, which is 360° and converted to inscribed angles it makes 180°, since we know the inscribed angle is half the value of the intercepted arc.

Same applies to opposite angle pair of ∠O and ∠Q.

Answer 2

Answer:

∠O and ∠Q and ∠R and ∠P

Step-by-step explanation:

Quadrilateral

A two-dimensional 4-sided shape whose interior angles sum to 360°.

Cyclic quadrilateral

A quadrilateral drawn inside a circle where every vertex touches the circumference of the circle.  

The opposite angles in a cyclic quadrilateral are supplementary (add up to 180°)

⇒ m∠O + m∠Q = 180°

⇒ m∠R + m∠P = 180°