Question

Find the value of each variable. PLEASE HELP ME

Answer 1

Given:

A quadrilateral DEFG inscribed in a circle.

$m\angle D=60^\circ, m\angle E=m^\circ, m\angle F=2k^\circ, m\angle G=60^\circ$

To find:

The value of variables $m$ and $k$.

Solution:

If a quadrilateral is inscribed in a circle then it is a cyclic quadrilateral. The opposite angles of a cyclic quadrilateral angle supplementary angles.

Quadrilateral DEFG inscribed in a circle. So, quadrilateral DEFG is a cyclic quadrilateral.

$m\angle D+m\angle F=180^\circ$                [Supplementary angle]

$60^\circ+2k^\circ=180^\circ$

$2k^\circ=180^\circ-60^\circ$

$2k^\circ=120^\circ$

Divide both sides by 2.

$k^\circ=\dfrac{120^\circ}{2}$

$k^\circ=60^\circ$

$k=60$

Similarly,

$m\angle E+m\angle G=180^\circ$

$m^\circ+60^\circ=180^\circ$

$m^\circ=180^\circ-60^\circ$

$m^\circ=120^\circ$

$m=120$

Therefore, the values of the variables are $m=120$ and $k=60$.