mbryant0610
Answered

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



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 ang class=

Answer :

mhanifa

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.

semsee45

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°

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