Question

How do I Find the value of y?

Answer 1

The triangles KLH and FLH are congruent by the hypotenuse leg theorem (HL theorem for short) because KL = LF is one pair of congruent legs and LM = LM is the pair of congruent hypotenuses. This theorem only works for right triangles.

By CPCTC (corresponding parts of congruent triangles are congruent), this means we can say that the bottom two angles KHL and FHL are congruent

So,

angle KHL = angle FHL

6y = 4y+18 ... substitution

6y-4y = 4y+18-4y .... subtract 4y from both sides

2y = 18

2y/2 = 18/2 ... divide both sides by 2

y = 9

Answer: 9

Answer 2

Yep y=9
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