Question Video: Finding the Measure of an Angle given Its Complementary Angle’s Measure Mathematics

Given that π‘šβˆ π΄π‘‚π΅ = 75Β°, what is π‘šβˆ π΅π‘‚πΆ?

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Video Transcript

Given that the measure of angle 𝐴𝑂𝐡 is 75 degrees, what is the measure of angle 𝐡𝑂𝐢?

In this question, we are given a figure and the measure of an angle in that figure. We need to use this to determine the measure of the other angle in the figure.

To answer this question, we can start by adding the two angles and the given measure onto the given diagram. We are told that the measure of angle 𝐴𝑂𝐡 is 75 degrees. We want to find the measure of angle 𝐡𝑂𝐢. Remember, the second point in the angle is the vertex of the angle. This can help us mark the angles on the diagram.

We can now note that these two angles are adjacent, since they share a vertex at 𝑂 and they have the ray from 𝑂 through 𝐡 as a common side and the angles do not overlap. We can then recall that the sum of the measures of adjacent angles is equal to the measure of the angle between their distinct sides. We can see in the diagram that this is a right angle, so its measure is 90 degrees. Since a right angle has a measure of 90 degrees, this means that the angles are complementary angles. And the sum of their measures is 90 degrees.

We can now solve this equation for the measure of angle 𝐡𝑂𝐢 by substituting in the measure of angle 𝐴𝑂𝐡 is 75 degrees. We then subtract 75 degrees from both sides of the equation to get that the measure of angle 𝐡𝑂𝐢 is equal to 90 degrees minus 75 degrees, which we can calculate is equal to 15 degrees.

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