Question

rectangle abcd has four right angles.

1. what is the sum of its angle measures?
2. move vertex a to a different location. which vertex - angle remains unchanged?

m∠a = 90°
m∠b = 90°
m∠c = 90°
m∠d = 90°

Explanation:

Step1: Recall angle - sum property of a quadrilateral

The sum of the interior angles of a quadrilateral is given by the formula $(n - 2)\times180^{\circ}$, where $n = 4$ for a quadrilateral. So, $(4 - 2)\times180^{\circ}=360^{\circ}$. Since a rectangle is a quadrilateral with four right - angles, the sum of its angle measures is $90^{\circ}+90^{\circ}+90^{\circ}+90^{\circ}=360^{\circ}$.

Step2: Consider the effect of moving vertex A

When vertex A is moved, the property of the rectangle's angles is based on the parallel - side and perpendicular - side relationships. The opposite sides of a rectangle are parallel. Vertex C is the opposite vertex of A. The angle at C is formed by the intersection of two sides that are parallel to the sides forming the angle at A. So, when A is moved, the angle at C remains unchanged as long as the figure remains a rectangle (preserving the parallel and perpendicular relationships).

Answer:

1. $360^{\circ}$
2. $\angle C$