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

Question

Find the measure of each marked angle. See Example 2supplementary angles with measures 10𝓍 + 7  and  7𝓍 + 3 degrees

Accepted Answer

Hey, everyone. Here we are asked to solve for the degree measure of the following supplementary angles. Where here we are given expression A as 13 X plus two and expression B is five X plus 16. Here we have four answer choice options. Answer choice A A is equal to degrees and B is equal to 61 degrees. Answer B A is equal to 61 degrees and B is equal to 119 degrees. Answer C A is equal to 54 degrees and B is equal to 36 degrees and answer D A is equal to 36 degrees and B is equal to 54 degrees. So the key with this problem is to recall that the sum of supplementary angles is 180 degrees. And we are told that expressions A and B are supplementary angles. So we know that A plus B is equal to 180. So now we just want to substitute in our given expressions for A and B into our equation. So we can solve for X. So we have expression A as 13 X plus two. Then plus expression B which is five X plus 16 and this is equal to 180. So now we just want to start combining like terms. So we have 18, X plus 18 is equal to 180. Now we need to solve for X by first subtracting 18 from both sides. So we find that 18 X is equal to 162. Now continuing to solve for X, we divide both sides by 18 and we find that X is equal to nine. And now we take this value of X and solve four hour degree measures by substituting X back into our expressions for A and B. So starting with expression, A again, recalling, we are given 13 X plus two and we now substitute in +94 X. So we have 13 multiplied by nine plus two. And now solving this expression, we get 119. So this tells us that A is going to be equal to 119 degrees. And now repeating this process with expression B, we again substitute in nine into the expression five X plus 16. And so we have five multiplied by nine plus 16. And now solving this expression, we get 61 and therefore we know that B is equal to 61 degrees. And now we have found the angles for A and B and so we are left with answer choice. A where again, A is equal to 119 degrees and B is equal to 61 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 2supplementary angles with measures 10𝓍 + 7 and 7𝓍 + 3 degrees

Key Concepts

Supplementary Angles

Algebraic Expressions

Solving Linear Equations

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