Question Video: Finding the Measure of an Angle given Its Arc’s Measure Using Another Inscribed Angle by Solving a Linear Equation Mathematics

Video Transcript

If the measure of angle 𝐵𝐴𝐷 is equal to two 𝑥 plus two degrees and the measure of angle 𝐵𝐶𝐷 is equal to 𝑥 plus 18 degrees, determine the value of 𝑥.

Let’s begin by adding the measure of angle 𝐵𝐴𝐷 and the measure of angle 𝐵𝐶𝐷 to the diagram. In doing so, we see that each of these inscribed angles is subtended from arc 𝐵𝐷. And so we quote one of the theorems that we use when working with inscribed angles. That is, angles subtended by the same arc are equal, or alternatively angles in the same segment are equal. This must mean that angle 𝐵𝐴𝐷 is equal to angle 𝐵𝐶𝐷. This allows us to form and solve an equation in 𝑥. The measure of angle 𝐵𝐴𝐷 is two 𝑥 plus two degrees, and the measure of angle 𝐵𝐶𝐷 is 𝑥 plus 18 degrees. So two 𝑥 plus two must be equal to 𝑥 plus 18.

To solve this equation for 𝑥, let’s begin by subtracting 𝑥 from both sides, giving us 𝑥 plus two equals 18. Finally, we can isolate the 𝑥 by subtracting two from both sides. 18 minus two is equal to 16. And so we’ve determined the value of 𝑥; it’s 16.