Video: Finding the Measure of an Angle given Its Corresponding Angle’s Measure

Find π‘šβˆ πΆ.

01:36

Video Transcript

Find the measure of angle 𝐢.

We can see from the diagram that the line 𝐴𝐡 is parallel to the line 𝐢𝐷. In this question, we need to calculate the measure of angle 𝐢. We begin by looking at the point 𝐴, noting that angles at a point or in a circle sum to 360 degrees. If we let the missing angle be π‘₯, then π‘₯ plus 123 plus 132 is equal to 360. Simplifying this gives us π‘₯ plus 255 is equal to 360. Subtracting 255 from both sides of this equation gives us π‘₯ is equal to 105. The missing angle at point 𝐴 is 105 degrees.

As mentioned previously, lines 𝐴𝐡 and 𝐢𝐷 are parallel. The line 𝐴𝐢 creates two cointerior or supplementary angles. As these sum to 180 degrees, the angle 𝑦 at point 𝐢 plus 105 must equal 180. Subtracting 105 from both sides of this equation gives us 𝑦 is equal to 75. We can therefore conclude that the measure of angle 𝐢 is equal to 75 degrees.

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