Question

Find the value of x.

Answer 1

Given:

A figure of a circle and inscribed quadrilateral JKLM.

$m\angle M=47^\circ,\angle K=(7x+21)^\circ$

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.

$m\angle M+m\angle K=180^\circ$

$47^\circ+(7x+21)^\circ=180^\circ$

$(7x+68)^\circ=180^\circ$

$(7x+68)=180$

Isolate the variable x.

$7x=180-68$

$7x=112$

$x=\dfrac{112}{7}$

$x=16$

Therefore, the value of x is 16.