Question

sam is building a picture frame. he cuts two wooden strips that cross each other and notices one of the angles is exactly 60°. he’s trying to figure out what the other angles must be. sam notices that one of the angles where his wooden strips cross is exactly 60°. what is the measure of the angle directly across from it (vertically opposite)? 30° 120° 90° 60° question 2 sam’s wooden strips form four angles where they intersect. if one angle measures 60°, what is the measure of an adjacent angle (next to the 60° angle)?

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal.

Step2: Determine the vertically - opposite angle

Since one angle is \(60^{\circ}\), the angle directly across from it (vertically opposite) is also \(60^{\circ}\).

Step3: Recall adjacent - angle property

Adjacent angles (linear - pair) sum to \(180^{\circ}\).

Step4: Calculate the adjacent angle

Let the adjacent angle be \(x\). Then \(x + 60^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-60^{\circ}=120^{\circ}\).

Answer:

For the vertically - opposite angle: \(60^{\circ}\). For the adjacent angle: \(120^{\circ}\).