JKL is an isosceles triangle with vertex angle K. Find the values of x and y if JK = 8x, KL= 13x - 15, the measure of angle KJL= (5y - 3), and the measure of angle JKL = 76

Answer 1

Bryce,

As you know, isosceles triangles have two angles (and thus two sides) that are congruent. The vertex angle is the angle that is not congruent to the other two.

Drawing the triangle would help you tremendously, as would looking up a picture of an isosceles triangle. We know that sides JK and LK are both the same length. Therefore we know that 8x = 13x - 15. A wee bit of algebra will help us simplify this expression and conclude that x = 3. From there, we know that sides JK and LK are both 24.

As I had said, the angle K is the angle that is different from the other two, and we are given that it is 76 degrees. (Angle K is the same as Angle JKL). So we know that the other two angles are both equal to 5y - 3. And we also know that a triangle is 180 degrees total.

180 - 76 = 104, so both of the congruent angles add up to 104. That means each of the two angles is equal to 52 degrees. That means that 5y - 3 = 52, which tells us that y = 11.

Hope this helps! :)

Answer 2

If JKL is an isosceles triangle with vertex angle K, then its JK and KL sides are the same length. We can make an equation with the lengths:

8x = 13x - 15

Solving the equation above yields that x = 3.

For the length of the angles we must star by remembering that the sum of the interior angles of any triangle is 180 degrees. Also, an isosceles triangle has two base angles that are the same. With this information we can write the equation:

2(5y - 3) + 76 = 180

The solution of the equation above is y = 11.

Answers: x = 3 and y = 11