Question

H is the midpoint of the angle bisector of angle LHN; HK = 3.9, and m angle JHL = 45°. Find m angle LHN and the length y.

A. m angle LHN = 45°, y = 3.9
B. m angle LHN = 90°, y = 7.8
C. m angle LHN = 45°, y = 7.8
D. m angle LHN = 90°, y = 3.9

Answer 1

The measure of angle LHN is 90°, and the length y is 7.8. This is because H bisects the angle and HK is given as 3.9, which is equal to HL, thus making y the sum of HL and HK.

Step-by-step explanation:

To find the measure of angle LHN and the length y, we can use the information given about the triangle formed. If H is the midpoint of the angle bisector of angle LHN, and HK = 3.9, with m angle JHL = 45°, then by the properties of an angle bisector in a triangle, angle LHN will be twice the measure of angle JHL.

Since m angle JHL is 45°, m angle LHN will be 90° (45° x 2). Because H is the midpoint of the angle bisector, HK will be equal to HL (the other segment of the angle bisector's bisected length). Therefore, the length y, which is the full length of the angle bisector HL plus HK, will be 3.9 + 3.9, totaling 7.8.