Question Video: Knowing that an Angle’s Bisector Divides it into 2 Equal Angles | Nagwa Question Video: Knowing that an Angle’s Bisector Divides it into 2 Equal Angles | Nagwa

# Question Video: Knowing that an Angleโs Bisector Divides it into 2 Equal Angles Mathematics

In the figure below, ๐โ ๐ต๐ด๐ถ = 30ยฐ. If the ray ๐ด๐ถ is an angle bisector, what is ๐โ ๐ต๐ด๐ท?

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### Video Transcript

In the figure below, the measure of angle ๐ต๐ด๐ถ is equal to 30 degrees. If the ray from ๐ด through ๐ถ is an angle bisector, what is the measure of angle ๐ต๐ด๐ท?

Letโs begin by identifying first angle ๐ต๐ด๐ถ. Itโs the angle enclosed by the line segments between ๐ต and ๐ด and ๐ด and ๐ถ. And so this angle here is 30 degrees. Now, weโre told that the line from ๐ด and passing through ๐ถ is an angle bisector. Now, a bisector cuts something in half, so an angle bisector divides an angle exactly in half. And this therefore means that angle ๐ถ๐ด๐ท must be equal to angle ๐ต๐ด๐ถ. Itโs also 30 degrees.

Now weโre looking to find angle ๐ต๐ด๐ท. Thatโs this one on our diagram. We can say that itโs equal to the measure of angle ๐ต๐ด๐ถ plus the measure of angle ๐ถ๐ด๐ท. Or alternatively since those angles are equal, itโs two times the measure of angle ๐ต๐ด๐ถ. Thatโs two times 30, which is equal to 60 degrees. The measure of angle ๐ต๐ด๐ท is 60 degrees. In general, we can say that an angleโs bisector divides it into two equally sized adjacent angles.

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