Question

find the values of the variables indicated below.

m =

degrees.

k =

degrees.

Explanation:

Step1: Use the property of cyclic quadrilaterals

In a cyclic quadrilateral, the sum of opposite angles is \(180^{\circ}\).
For cyclic quadrilateral \(DEFG\), \(\angle D+\angle F = 180^{\circ}\) and \(\angle E+\angle G=180^{\circ}\).
Since \(\angle D = 60^{\circ}\), then \(m+60^{\circ}=180^{\circ}\).

Step2: Solve for \(m\)

Subtract \(60^{\circ}\) from both sides of the equation \(m + 60^{\circ}=180^{\circ}\).
\(m=180^{\circ}- 60^{\circ}=120^{\circ}\).

Step3: Use the angle - sum property for the other pair of angles

Since \(\angle G = 60^{\circ}\), then \(2k+60^{\circ}=180^{\circ}\).

Step4: Solve for \(k\)

First, subtract \(60^{\circ}\) from both sides: \(2k=180^{\circ}-60^{\circ}=120^{\circ}\).
Then divide both sides by \(2\): \(k=\frac{120^{\circ}}{2}=60^{\circ}\).

Answer:

\(m = 120\) degrees.
\(k = 60\) degrees.