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

Question

Find the measure of each marked angle. See Example 2 supplementary angles with measures 6𝓍 - 4 and 8𝓍 - 12 degrees

Accepted Answer

Hey, everyone here we are asked to solve for the degree measure of the following supplementary angles. Where here we have expression A as 13 X minus two and expression B is five X minus 16. Here we have four answer choice options. Answer choice A A is equal to 39 degrees and B is equal to 141 degrees. Answer B A is equal to 141 degrees and B is equal to 39 degrees. Answer C A is equal to 76 degrees and B is equal to 14 degrees and answer D A is equal to 14 degrees and B is equal to degrees. So the key in solving this problem is to first recall that the sum of supplementary angles is 180 degrees. So this tells us that since our given expressions are supplementary angles, that expression A plus expression B must give us 180. So now we just want to substitute in our given expressions for A and B into this equation. And so we have 13 X minus two plus five X minus 16 is equal to 180. And now we just want to start combining like terms and then solving for X. So combining, we have 18, X minus 18 is equal to 180. Now solving for X, we add 18 to both sides. So we have 18, X is equal to 198. And now continuing to solve for X, we divide both sides by 18. And so we find that X is equal to 11. And now we need to take this X value and substitute it back in to our expressions for A and B so that we can solve for the angles. So starting with expression A again, recalling that we are given 13 X minus two and now we substitute in 11 4 X. So we have 13 multiplied by minus two. And now simplifying this expression, we find that A is going to be 141. So that tells us that A is equal to degrees. Now repeating this process with expression B again, recalling that B is five X minus and now substituting in 11, we have five multiplied by 11 minus 16. And now solving, we get that B is 39. So that tells us that B is 39 degrees. And with this, we have found the angles for A and B and so we are left with answer choice B where again, A is equal to 141 degrees and B is equal to 39 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 supplementary angles with measures 6𝓍 - 4 and 8𝓍 - 12 degrees

Key Concepts

Supplementary Angles

Setting Up and Solving Linear Equations

Substitution to Find Angle Measures

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