triangle degrees

Question

A right triangle, △JKL, is given with ∡KJL=30° and ∡JKL=90°. KM¯¯¯¯¯¯¯¯¯¯ is drawn such that L, K, and Mare collinear. Points J and M are joined by JM¯¯¯¯¯¯¯¯ with JM=JL. Find ∡JML.(1 point)

180°

60°

90°

30°

Answer 1

Since line L, K, and M are collinear, we can assume that M is extended to the left of M, and that line KM is tangent to line LK.

Sue to the collinearity, it is valid to assume that ∠JKM = 90º

If line JM is equal in length to line JL, and the two triangles JKM and JKL share side JK:

By the Side Angle Side postulate of congruence, the triangles are congruent.

Understanding this congruence, we can say that ∠KJL = ∠KJM = 30º

Using the All Angles Add to 180º theorem:

∠JML = ∠JMK = 180º - 90º - 30º = 60º

Answer 2

∠KJL = 30º Given

∠K = 90º Given

Then ∠KMJ = 30º sum of angles of a triangle = 180º

LJ = JM Given

Then Triangle LJM is isosceles

Then ∠JML = ∠KLJ = 60°