Question Video: Finding the Measure of the Base Angle in an Isosceles Triangle Mathematics • 11th Grade

Find 𝑚∠𝐵𝐴𝐶

02:26

Video Transcript

Find the measure of angle 𝐵𝐴𝐶.

Let’s take a look at the triangle 𝐴𝐵𝐶. We can observe that this triangle has two congruent sides marked 𝐴𝐵 and 𝐶𝐵. This tells us that triangle 𝐴𝐵𝐶 must be an isosceles triangle because these are defined as triangles that have two congruent sides. And there is another important property to do with the angles in an isosceles triangle. It is that in an isosceles triangle, the angles opposite the congruent sides are congruent. These are called the base angles.

Now, we are quite used to seeing isosceles triangles drawn like this, with both of the congruent base angles at the bottom of the triangle. However, this isn’t always the case, and it isn’t true in this triangle. We can always identify the base angles by remembering that they are opposite each of the congruent sides, so like this and like this. These base angles are congruent. We could even define both their measures with the same letter, for example, the letter 𝑥.

Now, given that the internal angle measures in a triangle sum to 180 degrees, we could work out what these two angle measures of 𝑥 are equal to. All three angle measures, that’s 𝑥, 𝑥, and 58 degrees, add to give 180 degrees. So two 𝑥 plus 58 degrees equals 180 degrees. And then two 𝑥 equals 180 degrees subtract 58 degrees, which is 122 degrees. Then, dividing both sides by two, we have that 𝑥 equals 61 degrees.

Now we know that triangle 𝐴𝐵𝐶 has two congruent angles with measures of 61 degrees and another angle with a measure of 58 degrees. We were asked to find the measure of angle 𝐵𝐴𝐶. So we can give the answer that this is 61 degrees.

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