Question

Q27. In the the given figure, ∠RQU = 65°. Find ∠y.​

Answer 1

Answer:

option c 230 degree

Step-by-step explanation:

since the angle subtended by the chord on the centre is double the angle subtended by the chord on any other part of the circle

Answer 2

$\large\underline{\sf{Solution-}}$

Given that

• ∠ RQU = 65°

Now,

AQU is a straight line.

∴ ∠ RQU + ∠ AQR = 180°

⇛ 65° + ∠ AQR = 180°

⇛ ∠ AQR = 180° - 65°

⇛ ∠ AQR = 115°

We know that,

Angle subtended at the centre by an arc is double the angle subtended by the same arc on the circumference of a circle.

So,

⇛ reflex ∠ AOR = 2 ∠ AQR

⇛ y° = 2 × 115°

⇛ y° = 230°

Hence,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underbrace{ \boxed{ \bf{ \: Option \: c) \: is \: correct}}}$

Additional Information :-

1. Angle in same segments are equal.

2. Perpendicular drawn from the centre bisects the chord.

3. Equal chords are equidistant from the centre.

4. Angle in semicircle is 90°

5. The sum of the opposite pair of angles of cyclic quadrilateral is 180°.

6. Exterior angle of a cyclic quadrilateral is equal to interior opposite angle.

7. Perpendicular bisector of the chord of a circle passes through the centre.

8. Equal chords subtends equal angles at the centre.