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=(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`.