Question

use the angle measures below to fill in each box in the diagram with the correct angle measure. 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 unknown angle

Let the first unknown angle adjacent to 40° be \(x\). We know that \(x + 40^{\circ}+130^{\circ}=180^{\circ}\) (a straight - line angle is 180°). So \(x=180^{\circ}-(40^{\circ} + 130^{\circ})=10^{\circ}\).

Step3: Calculate the second unknown angle

Let the second unknown angle adjacent to 65° be \(y\). We know that \(y+65^{\circ}+55^{\circ}=180^{\circ}\) (a straight - line angle is 180°). So \(y = 180^{\circ}-(65^{\circ}+55^{\circ})=60^{\circ}\).

Step4: Calculate the third unknown angle

Let the third unknown angle be \(z\). We know that \(z + 55^{\circ}+10^{\circ}=180^{\circ}\) (a straight - line angle is 180°). So \(z=180^{\circ}-(55^{\circ}+10^{\circ}) = 115^{\circ}\).

Step5: Calculate the fourth unknown angle

Let the fourth unknown angle be \(w\). We know that \(w+115^{\circ}+60^{\circ}=180^{\circ}\) (a straight - line angle is 180°). So \(w = 180^{\circ}-(115^{\circ}+60^{\circ})=5^{\circ}\).

Answer:

The angles (in order of the boxes starting from the box adjacent to 40° and moving clock - wise) are 10°, 60°, 115°, 5°.