Question

In the given diagram. O is the centre of the circle and PQR is a straight line. Find x.

(Step By Step)​

Answer 1

Given : O is the centre of the circle and PQR is a straight line.

To Find :  value of x

Solution:

∠PQT + ∠RQT = 180°

=> 80° + ∠RQT = 180°

=> ∠RQT = 100°

∠RQT + ∠TSR = 180° ( cyclic Quadrilateral )

=> 100° + ∠TSR = 180°

=>  ∠TSR =  80°

in Δ TOS

∠OTS = ∠OST   ∵ OS = OT = Radius

∠OTS +  ∠OST  + ∠TOS = 180°

=> 2∠OST + 50°= 180°

=>  2∠OST  = 130°

=> ∠OST  = 65°

∠TSR  = ∠OST + ∠OSR

=> 80° = 65° + x

=> x = 15°

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Answer 2

Step-by-step explanation:

✪ Given⤵

O is the centre of the circle and PQR is a straight line. Find x.

✪ To Find ⤵

Value of x ?

✪ Required Solution ⤵

➡ ∠PQT + ∠RQT = 180°

➡80° + ∠RQT = 180°

➡∠RQT = 180 - 80°

=>∠RQT = 100°

➡∠RQT + ∠TSR = 180° [cyclic quadrilateral ]

➡100° + ∠TSR = 180°

➡ ∠TSR = 180 + 100

=> ∠TSR = 80°

in ΔTOS

➡∠OTS = ∠OST ∵ OS - OT =Radius

➡∠OTS + ∠OST + ∠TOS = 180°

➡2∠OST + 50° = 180°

➡2∠OST = 130°

=> ∠OST = 65°

➡∠TSR = ∠OTS + ∠OSR

➡80° = 65 + x

=> x = 15°

.

Hope it helpful.. ✌️

@Somya2563