Question

QUESTION IS DOW BELOW 30 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP

Answer 1

The required solution is ∠RQT =  202°  and ∠QTS = 51°

What is a cyclic quadrilateral?

A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It is also called as inscribed quadrilateral.

Its main property is that the sum of opposite angles of inscribed quadrilateral is always 180 degrees.

Now, the given circle has a cyclic quadrilateral QRST in which it is given that  ∠RQT =  202° and ∠QRS = 129°

Since,sum of the opposite angles of a cyclic quadrilateral =  180°  

⇒∠QTS + ∠QRS = 180°

⇒ ∠QTS  + ∠129° = 180°

⇒ ∠QTS = 180° - ∠129°

⇒ ∠QTS = 51°

Hence,the requires angles are ∠RQT =  202° and ∠QTS = 51°.

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