Question

PQRS is a cyclic quadrilateral. if Q = 75° and R = 60°, find P and S​

Answer 1

• (ii) Option is correct.∠P and ∠S are 120° and 105° respectively.

Step-by-step explanation:

Given:-

• PQRS is a cyclic quadrilateral.
• Angle Q is 75°.
• Angle R is 60°.

To find:-

• Measure of angle P and angle S.

Solution:-

We know that,

Sum of pair of opposite angles of cyclic quadrilateral is 180°.

So,

➞ ∠S + ∠Q = 180°

➞ ∠S + 75° = 180°

➞ ∠S = 180° - 75°

➞ ∠S = 105°

Similarly,

➞ ∠P + ∠R = 180°

➞ ∠P + 60° = 180°

➞ ∠P = 180° - 60°

➞ ∠P = 120°

Therefore,

∠P and ∠S are 120° and 105° respectively.

_______

Two More properties of cyclic quadrilateral :-

• All four vertices of cyclic quadrilateral lies on circle.
• Sum of all interior angles of cyclic quadrilateral is 360°.

Answer 2

Answer:

$\huge \bf \: Solution$

• PQRS is a cyclic quadrilateral.
• Q = 75⁰
• R = 60⁰

Here,

$\sf \angle \: S + \angle \: Q= 180$

$\sf \therefore \angle \: s + 75 = 180$

$\sf \angle s = 180 - 75$

$\sf \angle \:s = 105 \degree$

Now finding P

$\sf \angle \: P + \angle \: R = 180$

$\sf \angle \: p + 60 = 180$

$\sf \angle \: p = 180 - 60$

$\sf \angle \: p = 120$

$\huge \fbox {S = 105}$

$\huge \fbox {P = 120}$

Let's verify

P + Q + R + S = 360

120 + 75 + 60 + 105 = 360

195 + 165 = 360

360 = 360