# Question Video: Finding the Measure of an Angle given Its Arcβs Measure Using Another Inscribed Angle by Solving a Linear Equation Mathematics

If πβ π΅π΄π· = (2π₯ + 2)Β° and πβ π΅πΆπ· = (π₯ + 18)Β°, determine the value of π₯.

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### Video Transcript

If the measure of angle π΅π΄π· is equal to two π₯ plus two degrees and the measure of angle π΅πΆπ· is equal to π₯ plus 18 degrees, determine the value of π₯.

Letβs begin by adding the measure of angle π΅π΄π· and the measure of angle π΅πΆπ· to the diagram. In doing so, we see that each of these inscribed angles is subtended from arc π΅π·. 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 π΅π΄π· is equal to angle π΅πΆπ·. This allows us to form and solve an equation in π₯. The measure of angle π΅π΄π· is two π₯ plus two degrees, and the measure of angle π΅πΆπ· is π₯ plus 18 degrees. So two π₯ plus two must be equal to π₯ plus 18.

To solve this equation for π₯, letβs begin by subtracting π₯ from both sides, giving us π₯ plus two equals 18. Finally, we can isolate the π₯ by subtracting two from both sides. 18 minus two is equal to 16. And so weβve determined the value of π₯; itβs 16.