Question

rectangle abcd has four right angles.

1. move vertex b to a different location. what is the sum of the angle measures of the quadrilateral? 360°
2. move vertices c and d to different locations. what is the sum of the angle measures of the quadrilateral? 360°
3. move each vertex one more time to a different location. what is the sum of the angle measures of the quadrilateral? 360°
4. make a conjecture. what is the sum of the angle measures of any quadrilateral? °

Explanation:

Step1: Recall polygon - angle sum formula

The sum of interior - angles of a polygon with \(n\) sides is given by \((n - 2)\times180^{\circ}\).

Step2: Identify \(n\) for a quadrilateral

For a quadrilateral, \(n = 4\).

Step3: Calculate the sum of interior angles

Substitute \(n = 4\) into the formula: \((4 - 2)\times180^{\circ}=2\times180^{\circ}=360^{\circ}\).

Answer:

360