Find the measure of each marked angle.

Question

Accepted Answer

Welcome back. I am so glad you're here. We're told in the following figure, solve for the value of the indicated angles in degree measure. We're given a figure with two intersecting lines which creates four angles, but only two of them are indicated that we need to solve for the two angles are vertical angles. One is labeled as X plus five degrees and the other, which is vertical to the first is labeled 20 X minus 23 degrees. Our answer choices are answer choice. A 57 degrees, 123 degrees. Answer choice B 57 degrees, 57 degrees. Answer choice C 75 degrees, 105 degrees and answer choice D degrees, 75 degrees. All right. What do we know about vertical angles? Well, we recall from previous lessons that they are congruent to one another, which means they're equal, we can set these two things equal to each other. Now setting aside the degrees for a moment so we can solve for X. So on one side of the equal sign, we've got 13 X plus five and that's equal to X minus 23. We can subtract 13 X from both sides bringing the XS to the right hand side of the equation. And at the same time, we can add 23 to both sides, bringing the constant terms to the left hand side of the equation. And none, the left 13 X minus 13 X is nothing. Five plus 23 is 28. And that's equal to on the right 20 X minus 13 X is seven X and negative 23 plus 23 is nothing. Now, we have 28 equals seven X. We can divide both sides by seven to solve for X and we get an X value of four, but we're not solving for X. We are trying to find the value of the angles. And so we can choose either of our degrees here. We can choose the 13 X plus five degrees and we can plug in for X this four. So this will be 13 multiplied not by X, but by four plus five degrees, 13 multiplied by four is 52. So we have 52 plus five degrees and 52 plus five is 57. So we know that these are both equal to 57 degrees because they are vertical angles and they are congruent meaning they are the same. We look at our answer choices and this matches with answer choice. B well done. We'll catch you on the next one.

Find the measure of each marked angle.

Key Concepts

Angle Measurement

Properties of Angles

Trigonometric Ratios

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