Question

Points P, Q and R lie on the circumference of a circle, centre O.
Angle PQR = 29°
Work out the size of the reflex angle POR.​

Answer 1

Answer:

To solve the problem, we join points Q and O.

Now, in ΔOQP,OP=OQ= radius.

⇒∠OPQ=∠OQP

Step-by-step explanation:

Since the sum of all angles in a triangle is 180*  

,∠POQ=(180−2x)  

 

Similarly, in ΔOQR,∠OQR=∠ORQ=y*

 

∴∠QOR=(180−2y)*  

 

∠POR=∠POQ+∠QOR

∴∠POR=(180−2x)  

+(180−2y)*  

 

=(360−2x−2y)*

hope this helps  

Answer 2

Given:

Points P, Q and R lie on the circumference of a circle with center O.

Angle PQR = 29°

To find:

The size of the reflex angle POR.

Solution:

• The sum of angles in a triangle formed by three points on a circle is 180°.
• Therefore, angle POR = (360° - angle PQR)/2 since it is a reflex angle.
• Substituting angle PQR = 29°, we get angle POR = (360° - 29°)/2 = 165.5°.

Therefore, the size of the reflex angle POR is 165.5°.

• When three points lie on a circle, the center of the circle lies at the intersection of the perpendicular bisectors of the chords formed by the three points.
• The angle at the center of a circle is twice the angle at any point on the circumference that subtends the same arc.
• The sum of angles in a triangle formed by three points on a circle is 180°.
• Using these properties, we can find the size of the reflex angle POR.

To learn more about circumference from the given link.

https://brainly.in/question/216005

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