SOLUTION: The sum of the measures of two complementary angles is 90 degrees. If one angle measures 21 degrees more than twice the measure of the other, find the measure of the smaller angle.

Question 566704: The sum of the measures of two complementary angles is 90 degrees. If one angle measures 21 degrees more than twice the measure of the other, find the measure of the smaller angle.
I am horrible at word problems! I can't get the problem out of what they asked. If the equation was in front of me I could solve it. Any help on how to identify how to make a word problem like this into an equation I can solve?
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The first sentence in this problem just states the definition of complementary angles. Translation: complementary angles are two angles whose measures add up to be 90 degrees.
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Then you are told "one angle ...". Stop here and ask yourself, "What is the value of that one angle?" The problem doesn't tell you a value for the measure of that one angle, so it is unknown to you. Let's just call that unknown measure X and it becomes something that you need to solve for.
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Next you are told "one angle is 21 degrees more than twice the measure of the other." Well, we've called one angle X, so this second angle is 21 degrees more than twice the measure of X. Twice the measure of X is 2 times X or 2X. And 21 degrees more than that means add 21 to 2X to get 2X + 21 as the measure of the second angle.
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So our 2 angles are X and 2X + 21. Since they are complementary angles we know that when you add the measures of these two angles the sum is 90 degrees. Let's add the measures together and set that equal to 90 as follows:
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X + 2X + 21 = 90
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Combine the X and 2X to get 3X and the equation then becomes:
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3X + 21 = 90
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Get rid of the 21 on the left side by subtracting 21 from both sides to get:
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3X = 90 - 21
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Doing the subtraction on the right side results in the equation becoming:
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3X = 69
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Now you can solve for X by dividing both sides by 3 (which is the multiplier of the X) to get:
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X = 69/3 = 23
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So we have now found the measure of one of the angles to be 23 degrees. That means that to find the measure of the other angle you can ask yourself how many degrees must its measure be so that when you add it to 23 degrees, the sum will be 90 degrees. You can get that by simply subtracting 23 from 90 to find that the measure of the second angle must be 67 degrees.
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Just as an added check, let's make sure that when you double the first angle that we found (23 degrees) and add 21 degrees from that, you also get 67 degrees that way. So double 23 degrees to get 46 degrees and add 21 to that and you do, in fact, get 67 degrees. It checks that way also.
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So the answer is that the measures of the two angles are 23 and 67 degrees.
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Don't let word problems confuse you too much. Just start by asking yourself "What is the unknown that I need to solve for?" Try to identify that unknown and call it X or something similar. Then try to identify how that unknown relates to the other information in the problem. In this problem the 2X + 21 was one piece of information you were given and the fact that the sum of the two angles needed to be 90 degrees was the other. From those we got the equation that allowed us to solve for X, and once you had X, you could solve for the measure of the other angle.
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Hope this helps you to understand this problem a little better. Keep trying. You'll eventually get the idea of how to break down word problems into small chunks that you can work with to solve them. Just takes time and patience and practice.
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