Find the measure of each marked angle. See Example 2complementary...

Question

Find the measure of each marked angle. See Example 2complementary angles with measures 3𝓍 ― 5  and  6𝓍 ― 40 degrees

Accepted Answer

Hey, everyone here we are asked to solve for the degree measure of the following complementary angles where here we have expression A four X minus seven. And we are also given expression B as 11 X minus 53. Here we have four answer choice options. Answer choice A A is equal to 57 degrees and B is equal to 123 degrees. Answer B A is equal to 123 degrees and B is equal to 57 degrees. Answer C A is equal to 57 degrees and B is equal to 33 degrees. And answer D A is equal to 33 degrees and B is equal to 57 degrees. So to begin this problem, the key is to recall that the sum of complementary angles is 90 degrees. And here we are told that A and B are complementary angles. So this tells us that A plus B or the sum of our two expressions must be equal to 90. And so now we just want to substitute in our given expressions into A and B so that we can solve four X. So we have four X minus seven plus 11 X minus is equal to 90. And now we just need to start combining like terms. So first we have four X plus 11 X which gives us 15 X, we then have negative seven plus negative which gives us negative 60. So so far we have 15 X minus 60 is equal to 90. And now just solving for X, we first add 60 to both sides. So we have 15, X is equal to 150. Now we divide both sides of the equation by 15 and we find that X is equal to 10. And now to solve for the degree measures, we have to substitute in this X value into each given expression. So starting with expression, A recalling, we have four X minus seven, we now substitute in 10, 4 X and we have four multiplied by minus seven. Now just simplifying we have 40 minus seven and simplifying further, we get 33. And so we find that A is equal to degrees. And now we repeat this process with our second given expression where again, we have 11 X minus 53 and now substituting in 10, 4 X, we have 11 multiplied by 10 minus 53. Simplifying we get 110 minus 53 and simplifying further, we get 57. So this tells us that B is then equal to degrees. So now we have solved for the degree measures of the given complementary angles. And so we are left with answer choice D where again, A is equal to 33 degrees and B is equal to 57 degrees. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Find the measure of each marked angle. See Example 2complementary angles with measures 3𝓍 ― 5 and 6𝓍 ― 40 degrees

Key Concepts

Complementary Angles

Algebraic Expressions

Solving Linear Equations

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