Question

In the given fig., O is the centre of the circle with chords AP and BP being produced
to R and Q respectively. If ZQPR = 35', find the measure of AOB​

Answer 1

Answer:

Hey mete here is ur Answer...

Step-by-step explanation:

∠APB and ∠QPR will be equal as they are vertically opposite angles.

∴∠APB=∠QPR=35∘

Also, we know angle made by a chord at point on the circle is half of the angle made at the center of the circle.

∴∠APB=  1/2 ∠AOB (Here, AB is the chord)

⇒∠AOB=2∠APB=2∗35=70∘

∴∠AOB=70∘  

Hope it helps u

Mark me as the Brainliest...

Answer 2

For the given circle having center O and angle QPR $35$°, the measure of angle AOB is $70$°.

Explanation:

• We know that two lines intersecting at a point make equal pairs of vertically opposite angles.
• Hence, here lines AR and BQ intersect at point P and angles QPR and APB are vertically opposite angles, $\angle APB= \angle QPR=35$
• Now it is given that AP and BP are the chords of the circle.
• Hence, APB is the angle subtended by the chord AB on the circumference of the circle.
• Now we know that the angle subtended by a chord at the center is double the angle subtended by the same chord at the circumference of the circle.
• Hence,    
•          $\angle AOB=2\angle APB\\->\angle AOB=2(35)\\->\angle AOB= 70\ deg.$  
• Therefore the measure of angle AOB is $70$°.