Question

rectangle abcd has four right angles.

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

Explanation:

Step1: Recall angle - sum formula for polygons

The sum of interior angles of a polygon with \(n\) sides is given by \((n - 2)\times180^{\circ}\). For a quadrilateral, \(n = 4\).

Step2: Calculate the sum

Substitute \(n = 4\) into the formula: \((4 - 2)\times180^{\circ}=2\times180^{\circ}=360^{\circ}\). The shape remains a quadrilateral regardless of the movement of its vertices.

Answer:

360