Question

Find the value of $x$ in the given figure in degrees.

Answer 1

According to Inscribed Angle Theorem, 'An inscribed angle is half of a central angle that subtends the same arc'.

$\therefore$ $\angle$$A$ is half of Central Angle $O$

$y=\frac{1}{2}{140}^{\circ }$

So, $\angle$$C=$ $y={70}^{\circ }$ ....$\left(i\right)$

We also know that 'The sum of opposite angles of a cyclic quadrilateral is 180 degrees'.

Since $\angle$$A$ and $\angle$$C$ are opposite to each other.

That is, $\angle$$A+$$\angle$$C={180}^{\circ }$

$\therefore$ $x+{70}^{\circ }={180}^{\circ }$ ...[From $eq.\left(i\right)$]

By subtracting ${70}^{\circ }$ from both the sides we get,

$x+{70}^{\circ }-{70}^{\circ }={180}^{\circ }-{70}^{\circ }$

$x={110}^{\circ }$