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Question Video: Finding the Measure of an Angle in a Triangle Subscribed in a Circle given the Other Two Angles Mathematics • 11th Grade

Given that ๐‘šโˆ ๐ต๐ถ๐‘€ = 49ยฐ, find ๐‘šโˆ ๐ต๐‘€๐ถ.


Video Transcript

Given that the measure of angle ๐ต๐ถ๐‘€ equals 49 degrees, find the measure of angle ๐ต๐‘€๐ถ.

Letโ€™s begin by filling in the angle measurements, being careful that we have got these values in the correct place. We are given that the measure of angle ๐ต๐ถ๐‘€ is 49 degrees. And the angle that we need to calculate is angle ๐ต๐‘€๐ถ. As we have a triangle, we could use the fact that the interior angle measures in a triangle add up to 180 degrees. However, we canโ€™t use this property straightaway because we also donโ€™t know the angle measure of angle ๐ถ๐ต๐‘€.

So letโ€™s apply some reasoning about the fact that this triangle is created in a circle. The line segments ๐‘€๐ถ and ๐‘€๐ต are both radii of the circle. And thatโ€™s helpful because that tells us that these two line segments will be congruent. This allows us to recognize that triangle ๐ต๐ถ๐‘€ is in fact an isosceles triangle. An isosceles triangle has two sides of equal length and two equal angle measures. So angle ๐ถ๐ต๐‘€ will be equal to angle ๐ต๐ถ๐‘€. In other words, they will both be 49 degrees.

Now, we can use the property that the interior angles in a triangle add up to 180 degrees. That means that the three angles of 49 degrees, 49 degrees, and the measure of angle ๐ต๐‘€๐ถ must add to give 180 degrees. We can simplify 49 degrees plus 49 degrees to give us 98 degrees. And then we can subtract 98 degrees from both sides of the equation, which gives us the answer that the measure of angle ๐ต๐‘€๐ถ is 82 degrees.

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