Question

In Triangle JKL, ∠J is congruent to ∠L. Triangle J K L is shown. Ray L K extends beyond point K to form an exterior angle that is labeled sixty-seven and eight tenths degrees. What is the measure of ∠L? Enter the correct answer in the box.

Answer 1

m<L =
`33.9^(o)`

Explanation:

Triangle JKL is an isosceles triangle, given that <J ≅ <L. An isosceles triangle has two of its angles and sides to be equal.

The exterior angle formed =
`67.8^(0)`

But,

<J + <L =
`67.8^(0)` (the sum of two opposite interior angles is equal to the exterior angle)

Let <J ≅ <L be represented by a, so that;

a + a =
`67.8^(0)`

2a =
`67.8^(0)`

a =
`(67.8^(o) )/(2)`

=
`33.9^(o)`

The measure of <L is m<L =
`33.9^(o)` (m<L =

Thus,

m<J ≅ m<L =
`33.9^(o)`