If the measure of angle one is 114 degrees and the measure of angle two equals two 𝑥 plus 21 degrees, find the value of 𝑥.
Looking at angle one and angle two in this image, we notice that they are the two angles opposite each other when two lines cross, which makes them vertical angles. And vertical angles are congruent to one another. Since angle one and angle two are vertical angles, the measure of angle one is equal to the measure of angle two. 114 degrees is equal to two 𝑥 plus 21 degrees.
To solve for 𝑥, we’ll let 114 be equal to two 𝑥 plus 21. And now we have a two-step equation we need to solve. We can do that by subtracting 21 from both sides of the equation. 114 minus 21 is 93. That means 93 equals two 𝑥. And to solve for 𝑥, we divide both sides of the equation by two. 93 divided by two is 46.5. And that means 𝑥 is equal to 46.5.