Question

In the figure given below $\square ABCD$ is a cyclic quadrilateral. Chord $AB\cong$ chord $BC$, chord $AD\cong$ chord $CD$. If $\angle ADC=3x^o$ and $\angle ABC=2x^o$, then find the measure of $\angle B$ and $\angle D$.

Answer 1

Here, $ABCD$ is a cyclic quadrilateral.

We know, in a cyclic quadrilateral, the sum of opposite angles are supplementary, i.e. ${180}^o$.

Here, $\angle B=2x^o$ and $\angle D=3x^o$ are opposite angles.

Then, $\angle B+\angle D={180}^o$

$⟹$ $2x^o+3x^o={180}^o$

$⟹$ $5x^o={180}^o$

$⟹$ $x^o=\frac{{180}^o}{5}$

$⟹$ $x^o={36}^o$.

Therefore,

$\angle B=2x^o=2\left({36}^o\right)={72}^o$

And

$\angle D=3x^o=3\left({36}^o\right)={108}^o$.