Video Transcript
Find the measure of angle
๐ต๐ด๐ถ.
Letโs take a look at the triangle
๐ด๐ต๐ถ. We can observe that this triangle
has two congruent sides marked ๐ด๐ต and ๐ถ๐ต. This tells us that triangle ๐ด๐ต๐ถ
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 isnโt always the
case, and it isnโt 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 ๐ฅ.
Now, given that the internal angle
measures in a triangle sum to 180 degrees, we could work out what these two angle
measures of ๐ฅ are equal to. All three angle measures, thatโs
๐ฅ, ๐ฅ, and 58 degrees, add to give 180 degrees. So two ๐ฅ plus 58 degrees equals
180 degrees. And then two ๐ฅ equals 180 degrees
subtract 58 degrees, which is 122 degrees. Then, dividing both sides by two,
we have that ๐ฅ equals 61 degrees.
Now we know that triangle ๐ด๐ต๐ถ
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 ๐ต๐ด๐ถ. So we can give the answer that this
is 61 degrees.
