The measures of two complementary angles have a ratio of 3 : 2. What is the measure of the larger angle?
1 answer:
<em>Question:</em> The measures of two complementary angles have a ratio of 3 : 2. What is the measure of the larger angle? ————— <em>Solution: </em> Call those two angles x and y , where x is the larger one. If they are complementary, then their sum equals 90° :x + y = 90° (i) Also, the ratio between x and y is 3 : 2 , so x 3 —— = —— y 2 Product of the extremes = product of the means: 2x = 3y2x – 3y = 0 (ii) Now, just solve this system of equations: x + y = 90° (i) 2x – 3y = 0 (ii) Solve it with elimination. Since you want to know the value of the larger angle, which is x , then eliminate the variable y by doing the following: Multiply the equation (i) by 3 ,3x + 3y = 270° (iii) 2x – 3y = 0 (ii) then add both equations, so you cancel out the variable y : 3x + 2x + 3y – 3y = 270° + 0 3x + 2x = 270° 5x = 270° 270° x = ——— 5x = 54° <——— this is the measure of the larger angle. I hope this helps. =) Tags: <span><em>system of linear equations elimination method solve complementary angles algebra geometry</em> </span>
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