Given:
A figure of a circle and inscribed quadrilateral JKLM.
[tex]m\angle M=47^\circ,\angle K=(7x+21)^\circ[/tex]
To find:
The value of x.
Solution:
The inscribed quadrilateral JKLM in the circle I is a cyclic quadrilateral and the opposite angles of a cyclic quadrilateral are supplementary angles.
Angle M and angle K are opposite angles of a cyclic quadrilateral, it means they are supplementary angles and their sum is 180 degrees.
[tex]m\angle M+m\angle K=180^\circ[/tex]
[tex]47^\circ+(7x+21)^\circ=180^\circ[/tex]
[tex](7x+68)^\circ=180^\circ[/tex]
[tex](7x+68)=180[/tex]
Isolate the variable x.
[tex]7x=180-68[/tex]
[tex]7x=112[/tex]
[tex]x=\dfrac{112}{7}[/tex]
[tex]x=16[/tex]
Therefore, the value of x is 16.