Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Find m∠1 and m∠3 in the kite. The diagram is not drawn to scale.
To find m∠1 and m∠3 in the kite, we need to take into account the following properties:
1. In a kite, the diagonals are perpendicular bisectors of each other, meaning they divide each other into segments that are equal in length.
2. The angles formed at the intersection of the diagonals are equal in measure.
Given this information, let's denote the measures of ∠1 and ∠3 as x. Since the diagonals of the kite bisect each other, each segment of the diagonal will be of equal length. Let's denote the length of each segment as y.
From the properties of the kite, we have:
x + x + 90 = 360 (Sum of angles in a quadrilateral)
2x + 90 = 360
2x = 270
x = 135
Therefore, m∠1 = m∠3 = 135 degrees.