# In the Figure Given Below 'O' is the Centre of the Circle. If Qr = Op and ∠Orp = 20°. Find the Value of 'X' Giving Reasons - Mathematics

In the figure given below 'O' is the centre of the circle. If QR = OP and ∠ORP = 20°. Find the value of 'x' giving reasons

#### Solution

Now,

OP = QR....given

So,OP =  OT = OQ = QR

In ΔRQP

RQ = QO

So angleQRO = angleQOR = 20^@

So by sum of angles in ΔRQP

angleRQO = 140^@

Now

angleRQO + angleOQP = 180^@  .....linear pair

angle OQP = 40^@

in ΔPOQ

So angleQPO - angle OQP = 40^@

So by sumof angle in ΔOQP

anglePOQ - 100^@

Now

anglePOT + anglePOQ +angle QOR = 180^@ ......angles in straight line

x= 60^@

Concept: Circumscribing and Inscribing a Circle on a Triangle
Is there an error in this question or solution?