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VashaNatasha [74]
3 years ago
8

Find the value of each variable. PLEASE HELP ME

Mathematics
1 answer:
Nuetrik [128]3 years ago
6 0

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.

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