MathematicsWhich of the following is the values of y and z, where O denotes the centre of the circle.

Which of the following is the values of $y$ and $z$ , where $O$ denotes the centre of the circle.

Consider the given figure,

In a cyclic quadrilateral sum of opposite angles are supplementary.
So, from the figure,

∠ y + 35^{o} = 180^{o}

\Rightarrow ∠ y = 180^{o} - 35^{o}

\Rightarrow ∠ y = 145^{o}

The angle subtended by a chord to the circumference of a circle is half of that subtended to the centre.
Then,

∠ z = 2 \times ∠ y

\Rightarrow ∠ z = 2 \times 145^{o}

\Rightarrow ∠ z = 290^{o}

Hence, the measure of

∠ y = 145^{o}

and

∠ z = 290^{o}

.
Therefore, option 3 is correct.

JEE