Question

drag an angle measure into each box to fill in the diagram.

Explanation:

Step1: Recall angle - sum property of a circle

The sum of angles around a point is 360°.

Step2: Calculate the first missing angle

Let the first missing angle be \(x\). We know that \(x + 40^{\circ}+65^{\circ}+55^{\circ}=180^{\circ}\) (since they form a straight - line angle which is 180°). So \(x=180^{\circ}-(40^{\circ}+65^{\circ}+55^{\circ})=180^{\circ}-160^{\circ}=20^{\circ}\).

Step3: Calculate the second missing angle

Let the second missing angle be \(y\). We know that \(y + 65^{\circ}=130^{\circ}\), so \(y = 130^{\circ}-65^{\circ}=65^{\circ}\).

Step4: Calculate the third missing angle

Let the third missing angle be \(z\). We know that \(z+55^{\circ}+20^{\circ}=180^{\circ}\) (since they form a straight - line angle). So \(z = 180^{\circ}-(55^{\circ}+20^{\circ})=105^{\circ}\).

Step5: Calculate the fourth missing angle

The fourth missing angle is \(180^{\circ}-105^{\circ}=75^{\circ}\).

Answer:

From top - right in clock - wise order: \(20^{\circ}\), \(65^{\circ}\), \(105^{\circ}\), \(75^{\circ}\)