Find the measure of each marked angle. See Example 2

complementa...

Question

Find the measure of each marked angle. See Example 2

complementary angles with measures 9𝓍 + 6  and  3𝓍 degrees

Accepted Answer

Hey, everyone here we are asked to solve for the degree measure of the following complementary angles. Where here we are given expression A five X plus six and expression B seven X. Here we have four answer choice options. Answer choice A, A is equal to 79 degrees and B is equal to 101 degrees. Answer B A is equal to 101 degrees. And B is equal to 79 degrees. Answer C A is equal to 41 degrees and B is equal to 49 degrees. Answer D A is equal to 49 degrees and B is equal to 41 degrees. So the key in solving this problem is to recall that the sum of complementary angles is 90 degrees. So here we are told that our two given expressions are complementary angles. So that tells us that expression A plus expression B is equal to 90. And now we just want to substitute in the given expressions for A and B into this equation so that we can solve for X. So we have five X plus six plus seven X is equal to 90. And now we just want to start combining like terms. So we have five X plus seven X which gets us 12 X plus six is equal to 90. And now we just want to start solving for X by first subtracting six from both sides. And so we have 12, X is equal to 84. Now we just need to divide both sides by 12 and we find that X is equal to seven. And now we need to take this X value and substitute them back in to our given expressions for A and B. So starting with expression, A recalling we have five X plus six. Well, we now substitute in 74 X so we have five multiplied by seven plus six. Now just simplifying, we have 35 plus six and summing the two values we get 41. So this tells us that A is equal to degrees. And now with our expression for B again, recalling that we have seven X, we now have seven multiplied by seven which gives us 49. So this tells us that B is equal to 49 degrees. And with this, we have found the angles for A and B and so we are left here with answer choice C where again, A is equal to 41 degrees and B is equal to 49 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 2 complementary angles with measures 9𝓍 + 6 and 3𝓍 degrees

Key Concepts

Complementary Angles

Algebraic Expressions

Solving Linear Equations

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