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.
