Cyclic Quadrilateral Angle Calculation
<p>In a cyclic quadrilateral, the sum of opposite angles is 180 degrees.</p>
<p>Given angle K = 120 degrees, we find the opposite angle M, which is 110 degrees + x.</p>
<p>120 degrees + (110 degrees + x) = 180 degrees</p>
<p>230 degrees + x = 180 degrees</p>
<p>x = 180 degrees - 230 degrees</p>
<p>x = -50 degrees</p>
<p>Since an angle cannot be negative in this context, we need to reconsider the equation for opposite angles.</p>
<p>We use the property that the exterior angle is equal to the opposite interior angle.</p>
<p>Thus the exterior angle at vertex L is 120 degrees which is equal to angle N + angle M.</p>
<p>Angle N is 70 degrees because it is the base angle of the isosceles triangle KLN (angle K is 120 degrees).</p>
<p>120 degrees = 70 degrees + angle M</p>
<p>Angle M = 120 degrees - 70 degrees</p>
<p>Angle M = 50 degrees</p>
<p>Therefore, x = 50 degrees</p>
