Question

I know the measure of angle m is 100 degrees. I did this multiple times and J and L are not 80 degrees so what are the measures of angles L and J?

Answer 1

`m\angle L = 100^(\circ)`.

`m\angle J = 80^(\circ)`.

`m\angle M = 100^(\circ)`.

Explanation:

Since segment
`JM` is parallel to segment
`KL`, quadrilateral
`JKLM` is a trapezoid.

Segment
`JK` and segment
`LM` (the two legs of this trapezoid) are equal in length. Hence, trapezoid
`JKLM` would be an isoscele trapezoid. By symmetry,
`m\angle L = m \angle K = 100^(\circ)`.

Line
`JK` traverses line
`JM` and line
`KL`.
`\angle J` and
`\angle K` are a pair of consecutive interior angles as they are both between
`JM\!` and
`KL\!` and are on the same side of the traversal,
`JK\!`.

Since line
`JM` is parallel to line
`KL`, any pair of consecutive interior angles between these two lines would add up to
`180^(\circ)` (supplementary angles.) Thus,
`\angle J` and
`\angle K` are supplementary angles;
`m\angle J + m\angle K = 180^(\circ)`.

Since
`m\angle K = 100^(\circ)`,
`m\angle J = 180^(\circ) - m\angle K = 180^(\circ) - 100^(\circ) = 80^(\circ)`.