In the given diagram. O is the centre of the circle and PQR is a straight line. Find x.
(Step By Step)
Answers
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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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.. ✌️