Question Video: Finding the Measure of Base Angles in Isosceles Triangles | Nagwa Question Video: Finding the Measure of Base Angles in Isosceles Triangles | Nagwa

# Question Video: Finding the Measure of Base Angles in Isosceles Triangles Mathematics • Second Year of Preparatory School

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Find πβ πΆπ΅π΄ and πβ π·π΄πΆ.

03:11

### Video Transcript

Find the measure of angle πΆπ΅π΄ and the measure of angle π·π΄πΆ.

The first angle measure that we need to find is that of angle πΆπ΅π΄. This is part of the larger triangle π΄π΅πΆ.

We observe that triangle π΄π΅πΆ has two congruent line segments marked: π΄πΆ and π΅πΆ. That means that this is an isosceles triangle, as an isosceles triangle is defined as a triangle that has two congruent sides. We can then use the isosceles triangle theorem, which states that in an isosceles triangle, the angles opposite the congruent sides are congruent. In triangle π΄π΅πΆ, these two congruent base angles will be angle πΆπ΄π΅ and angle πΆπ΅π΄. If we defined these angles to have a measure of π₯ degrees, then we can write that π₯ degrees plus π₯ degrees plus 38 degrees equals 180 degrees.

Remember, we can set these three angle measures equal to 180 degrees because the sum of the internal measures in a triangle is 180 degrees. We can then simplify this by collecting the like terms and then subtracting 38 degrees from both sides, which gives us that two π₯ degrees is equal to 142 degrees. Dividing through by two, we have that π₯ is equal to 71 degrees. So now we know the measure of both the base angles in triangle π΄π΅πΆ. They are both 71 degrees. And thatβs the answer for the first angle, since the measure of angle πΆπ΅π΄ is 71 degrees.

Now letβs consider the second angle measure, which is the measure of angle π·π΄πΆ. Observe that we have this angle π·π΄πΆ and the angle π·π΄π΅, which together form the larger angle πΆπ΄π΅ whose measure we have already calculated as 71 degrees. If we knew the measure of angle π·π΄π΅, we could calculate the measure of angle π·π΄πΆ.

Letβs take a closer look at triangle π΄π΅π·. It has three congruent sides. And that means that triangle π΄π΅π· is an equilateral triangle. And we know that an equilateral triangle has all three angles congruent, which means they are all 60 degrees. So, the measure of angle π·π΄πΆ is equal to 71 degrees minus 60 degrees, which is 11 degrees.

Therefore, we can give the answers to both parts of the question. The measure of angle πΆπ΅π΄ is 71 degrees, and the measure of angle π·π΄πΆ is 11 degrees.

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