### Video Transcript

In the figure, ๐ฟ๐ป is the midsegment of trapezoid ๐น๐บ๐ฝ๐พ. What is the value of ๐ฅ?

So we have a diagram of a trapezoid. And weโre told that the line segment ๐ฟ๐ป is its midsegment. What does this is mean? Firstly, the midsegment of a trapezoid is parallel to each base. So in this case, thatโs the lines ๐น๐บ and ๐พ๐ฝ.

Secondly, the midsegment connects the midpoints of the legs of the trapezoid. We can see the ๐ฟ and ๐ป are the midpoints of the two legs because the line segments ๐น๐ฟ and ๐ฟ๐พ are equal in length and also the line segments ๐บ๐ป and ๐ป๐ฝ are equal to each other in length.

Weโve been told the length of one of the bases of the trapezoid ๐พ๐ฝ and the length of the midsegment. The value weโre looking to calculate, ๐ฅ, is the length of the second base of the trapezoid ๐น๐บ.

In order to answer this question, we need to recall the trapezoid midsegment theorem. It tells us this. The measure of the midsegment of a trapezoid is half the sum of the lengths of the bases. In this trapezoid, the bases are 23.6 and ๐ฅ. The length of the midsegment is 18.6. So we can express this as an equation. Half the sum of the length of the bases, so thatโs ๐ฅ plus 23.6 over two, is equal to 18.6.

To find ๐ฅ, we now need to solve this equation. The first step is to multiply both sides of the equation by two. This gives ๐ฅ plus 23.6 is equal to 37.2. The final step in solving this equation is to subtract 23.6 from both sides. This gives ๐ฅ is equal to 13.6. So we found the value of ๐ฅ. Itโs 13.6.

Remember, the key fact we used in this question was the trapezoid midsegment theorem, which tells us that the measure of the midsegment of a trapezoid is half the sum of the lengths of the bases.