Find the perimeter of the square 𝐴𝐵𝐶𝐷 below and determine the measure of angle 𝐸𝐶𝐷 if the measure of angle 𝐵𝐶𝐸 equals 70 degrees.
There are two parts to this question. The first one is to find the perimeter and the second one is to find the missing angle 𝐸𝐶𝐷. So let’s start by recalling that perimeter is the distance all the way around the outside edge of a shape. The first thing to do is to recall that a square has four sides of equal length. That means that the four sides of this square will all be of 60 centimeters. In order to find the perimeter, we can add 60, 60, 60, and 60, or we can work out four multiplied by 60. Either way, we’ll get an answer of 240. The units here will be length units of centimeters.
Now that we found the perimeter, let’s see if we can find the measure of angle 𝐸𝐶𝐷. We’re given that the measure of angle 𝐵𝐶𝐸 is 70 degrees, and we could fill this onto the diagram. We’ll need to recall another fact about the angles in a square. All the interior angles in a square are 90 degrees. So, to find angle 𝐸𝐶𝐷, we take angle 𝐷𝐶𝐵, which is 90 degrees, and subtract the angle 𝐵𝐶𝐸, which is 70 degrees, leaving us with 20 degrees.
We can give the two answers to the question: the perimeter is 240 centimeters, and angle 𝐸𝐶𝐷 is 20 degrees.