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

Given that π‘šβˆ πΉπΈπ· = 14Β° and π‘šβˆ πΆπ΅π΄ = 2π‘₯ βˆ’ 96Β°, calculate the value of π‘₯.

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Video Transcript

Given that the measure of angle 𝐹𝐸𝐷 is equal to 14 degrees and the measure of angle 𝐢𝐡𝐴 is equal to two π‘₯ minus 96 degrees, calculate the value of π‘₯.

So let’s look at the diagram. We quickly see that arc 𝐴𝐢 is congruent to arc 𝐷𝐹. And we know that inscribed angles subtended by congruent arcs are going to be equal in measure. So this means that angle 𝐴𝐡𝐢 is going to be equal in measure to angle 𝐷𝐸𝐹. We’re in fact told that the measure of angle 𝐴𝐡𝐢 or 𝐢𝐡𝐴 is two π‘₯ minus 96. And the measure of angle 𝐹𝐸𝐷, which is the same as 𝐷𝐸𝐹, is 14 degrees. Since these angles are equal, we can form and solve an equation in π‘₯. That is, two π‘₯ minus 96 equals 14. To solve for π‘₯, we add 96 to both sides, giving us two π‘₯ is equal to 110. And finally, we divide through by two, and that gives us π‘₯ is equal to 55. And so given the information about angles 𝐹𝐸𝐷 and 𝐢𝐡𝐴, we can deduce that π‘₯ is equal to 55.

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