Question Video: Solving Word Problems Using Properties of Trapezoids

Given that 𝐽𝐾𝐿𝑀 is a trapezoid and π‘šβˆ π‘€ = 68Β°, find π‘šβˆ πΎ.

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Video Transcript

Given that 𝐽𝐾𝐿𝑀 is a trapezoid and the measure of angle 𝑀 equals 68 degrees, find the measure of angle 𝐾.

Looking at our diagram, we can see that there is a pair or parallel sides which confirms that it is a trapezoid. In countries outside of the US and Canada, you may know a quadrilateral with a pair of parallel sides as a trapezium. We can also see in our diagram that we have two sides, the side 𝐽𝑀 and the side 𝐾𝐿, which are both labelled with 39. This means that these two sides are congruent. And it also tells us one important fact about this trapezoid. And that is that 𝐽𝐾𝐿𝑀 is an isosceles trapezoid. Isosceles trapezoids have a pair of parallel sides. And they also have nonparallel sides which are congruent. In an isosceles trapezoid, the lower base angles are congruent and the upper angles are congruent.

So in our diagram, we’re told that the measure of angle 𝑀 is 68 degrees. So using the fact that the lower base angles are congruent, we now know that the angle 𝐿 is 68 degrees. And we’re asked to calculate the measure of angle 𝐾. To do this, we can use the fact that we have a pair of parallel lines. When we have parallel lines, the consecutive interior angles are supplementary, which means they add up to 180 degrees. We can see that angle 𝐾 and angle 𝐿 are consecutive interior angles. So we can write that the measure of angle 𝐾 plus the measure of angle 𝐿 is equal to 180 degrees. And since the measure of angle 𝐿 is 68 degrees, then to find the measure of angle 𝐾, we subtract 68 degrees from both sides of our equation. So the measure of angle 𝐾 is 112 degrees.

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