Find the measurement of angle 𝐴.
We’re given a quadrilateral, a four-sided shape. And we’re asked to find the measurement of one of its angles, angle 𝐴. We’re told that this angle is five 𝑥 degrees. And angle 𝐷 measures 𝑥 degrees. We’re also told that angles 𝐵 and 𝐶 are both right angles. Angles 𝐵 and 𝐶 each measure 90 degrees. We can use this information to help us find 𝑥, and then five 𝑥.
An important fact we need to know to help us do this is that the sum of the angles in a quadrilateral is 360 degrees. In other words, angle 𝐴 plus angle 𝐵 plus angle 𝐶 plus angle 𝐷 equals 360 degrees. So, five 𝑥 degrees, which is the measurement of angle 𝐴, plus two lots of 90 degrees, which is the measurements for angles 𝐵 and 𝐶, plus 𝑥 degrees, the measurement for angle 𝐷, equals 360 degrees.
We know that the total of the two right angles is 180 degrees because two lots of 90 is 180. If we take this 180 degrees away from 360, because all the angles inside the quadrilateral total 360 degrees, that would tell us how much angles 𝐴 and 𝐷 add up to. 360 take away 180 is 180. Now, we know that 𝑥 plus five 𝑥 equals 180 degrees. 𝑥 plus five 𝑥 is six 𝑥. If six 𝑥 is 180 degrees, to find one lot of 𝑥, we need to divide 180 by six.
We know that 18 divided by six is three. So, 180 divided by six is 30. Now, we know what the value of 𝑥 is. We can calculate the value of five 𝑥. What is five times 30? We know that five times three is 15, so five times 30 is a 150. The measurement of angle 𝐴 is 150 degrees. We know that the sum of the angles in a quadrilateral is 360 degrees and the angles 𝐵 and 𝐶 totaled 180 degrees. This meant that six 𝑥, or angles 𝐴 and 𝐵, totaled 180 degrees. We knew that if six 𝑥 was 180, 𝑥 was equal to 30, and so five 𝑥 is equal to 150. The measurement of angle 𝐴 is 150 degrees.