Question Video: Finding the Measure of an Angle given Its Complementary Angleโ€™s Measure Mathematics

Find the perimeter of the square ๐ด๐ต๐ถ๐ท below, and determine ๐‘šโˆ ๐ธ๐ถ๐ท if ๐‘šโˆ ๐ต๐ถ๐ธ = 70ยฐ.


Video Transcript

Find the perimeter of the square ๐ด๐ต๐ถ๐ท below and determine the measure of angle ๐ธ๐ถ๐ท if the measure of angle ๐ต๐ถ๐ธ 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 ๐ธ๐ถ๐ท. So letโ€™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, weโ€™ll get an answer of 240. The units here will be length units of centimeters.

Now that we found the perimeter, letโ€™s see if we can find the measure of angle ๐ธ๐ถ๐ท. Weโ€™re given that the measure of angle ๐ต๐ถ๐ธ is 70 degrees, and we could fill this onto the diagram. Weโ€™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 ๐ธ๐ถ๐ท, we take angle ๐ท๐ถ๐ต, which is 90 degrees, and subtract the angle ๐ต๐ถ๐ธ, 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 ๐ธ๐ถ๐ท is 20 degrees.

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