Learn about Complementary and Supplementary Angles In this lesson, let’s learn about complementary and supplementary angles. So, just real quick before we try and tackle problems. If we have an angle, let’s say this angle measures 63o, the complement of this angle is an angle that measure 27o because the sum of these, 63 plus 27o is 90o. So, complementary angles equals 90o which is the sum of complementary angles equals 90o. Similarly, the sum of supplementary angles equals 180o. Do you know how I remember complementary? C is for corner. So, it’s a corner. Sum for supplementary, straight line, 180 degrees. Supplementary is straight line, complementary is a corner which is at 90-degree angle. Enough for teaching. Let’s actually try and do a couple of problems. It says find the complement of angle E. Angle E is given to us as 7x–12. What am I told? The complement of E, so measurement of angle E plus measurement of complement of E. Sum of E and the complement of E will be 90 degrees. What do I know? The measurement if E is 7x–12 plus measurement of I’m going to call it complement of E, equals 90 degrees. So, all of that means is if I want to solve this equation, what am I given? I can add 12 to both sides and then add 7x to subtract 7x from both sides. What will I get? Well, if add 12 this will become zero. If I subtract 7x, this will become zero. So, the measurement of complement of angle E will be 90 + 12 - 7x or 130 minus 7x. So, whatever the complement is, it will be 102 degrees minus 7x. Complement of this is this. Remember, the key thing to remember, the sum of any angle and its complement is 90 degrees. Similarly, let’s find the supplement of angle F. What is angle F? Angle F equals 116.5 degrees. So, angle F plus supplement of angle F equals 180 degrees. So, this becomes 116.5 plus question mark equals 180 degrees. I can subtract one and 6.5 from both sides. What do I get? That the supplement of angle F which is this angle is going to be the supplement of angle F is 180 minus 116.5 is 63.5 degrees. Remember, this plus this equals 180. The rest of it is solving a simple equation. Let’s do a slightly more complicated problem. It says light passing through a fiber optic cable reflects off the wall. So it’s light that’s coming here reflecting off the wall. That angle one is congruent to angle two. So, this angle and this angle are the same. Angle one and three are complementary. So, this plus this is complementary. Two and four are complementary which means they are 90 degrees. We’re given angle one as 38 degrees. If angle one is 38, angle two is 38 as well because they are congruent. So, what is angle three? Well, I know 38 degrees which is this part plus angle three equals 90 degrees because they are a complementary angles. If they are complementary angles, one plus three will be 38 plus angle three will be 90 degrees or angle three will be 90 minus 38 or 62 degrees. So, this will be 62 degrees. Similarly, when I look at these, 38 degrees plus angle four equals 90 degrees because they are complementary as well which means angle four is 90 minus 38 which is again 62 degrees. So, angle three and four are 62 degrees. Angle one and two are 38 degrees. We found all the angles. Angle two equals 38 degrees. Angle three equals 62; angle four equals 62.