Question

What is m∠LQK?

Answer 1

The angles GQL and LQK make up the larger angle GQK. We know that GQK is 90 degrees because we are told that GQH is 90 degrees.
We can express the information above in this relationship:
\[\angle{GQK} = \angle{GQL} + \angle{LQK}\]
\[90 = 3n + \left( 4n-15 \right)\]
So you can solve for n, then plug that into the expression for angle LQK to find that angle's measurement:
\[\angle{LQK} = 4n-15\]

Answer 2

53 i think

Answer 3

Close...
What did you get for your value of n from this equation?
\[90 = 3n + \left( 4n - 15 \right)\]

Answer 4

i got -24 is that right?

Answer 5

Nope, it should be a positive number.
I'll combine the "n" terms for you to get you started:
\[90 = 3n + \left( 4n-15 \right)\]
\[90 = 3n + 4n -15\]
\[90 = 7n - 15\]
Can you solve for "n" now?

Answer 6

n = 15

Answer 7

Yep! Now all you have to do is plug that value for n into the equation for angle LQK:
\[\angle{LQK} = 4n-15\]