I need help on this homework question
KL and KJ are opposites rays.Angle 1 is congruent to angle 2 and KM bisects angle NKL.If angle JKN=9x+5 and angle MKL=2x+3,what is angle MKN?
Please help me....
Don't know what angles 1 and 2 are, but
angles JKN + NKM + MKL = 180
MKN = NKM, since KM bisects angle NKL
9x+5 + 2x+3 + 2x+3 = 180
13x + 11 = 180
13x = 169
x = 13
MKN = 2x+3 = 29
Thank you!!!
S is in the interior of ∠PQR
m∠PQS = 3X +11
m∠SQR = 110
m∠PQR = 16x + 4
Find the m∠PQS:
To find angle MKN, we need to use the information given in the question.
First, let's identify the given angle measures:
- Angle JKN = 9x + 5
- Angle MKL = 2x + 3
We also know that KL and KJ are opposite rays, meaning they form a straight line. Therefore, angle JKL and angle MKL are supplementary angles (their measures add up to 180 degrees).
Now, let's use the fact that KM bisects angle NKL. When a line bisects an angle, it divides the angle into two congruent angles. Therefore, angle MKL is congruent to angle NKL.
Since angles MKL and NKL are congruent, we can set their measures equal to each other:
2x + 3 = angle NKL
Next, we can use the fact that angle JKL and angle MKL are supplementary to find the measure of angle JKL. Since angle JKL and angle MKL are supplementary, their measures add up to 180 degrees:
angle JKL + angle MKL = 180 degrees
Angle JKL + (2x + 3) = 180 degrees
Now, we have two equations:
2x + 3 = angle NKL
angle JKL + (2x + 3) = 180 degrees
We need to substitute angle NKL with angle MKL since they are congruent:
angle JKL + (2x + 3) = 180 degrees
angle JKL + (2x + 3) = 180 degrees
Now, we can solve this system of equations to find the value of x, which will lead us to the measure of angle MKN.
This is where you would need to provide any additional information or clarify the problem to proceed further with solving for x and angles.