m and n are supplementary angles, which means they are 180 degrees. Since the left side of m is 75 degrees, the right side must be 105 because it has to equal 180 degrees (180 - 75 = 105).
Since the left side of m (75 degrees) and the right side of n (10x + 15 degrees) are criss-cross from each other they are opposites. The left side of m and the left side of n are equal while the right side of m and the right side of n are equal. In other words, (10x + 15 degrees) is equal to 105 because the one directly above it is 105. We can make an equation to find x knowing this.
10x + 15 = 105
10x + 15 - 15 = 105 - 15
10x = 90
x = 9
Check:
10(9) + 15 = 105
90 + 15 = 105
105 = 105
m∠C is read as "the measure of angle C." From the picture we see that angle B is a right angle which makes it 90 degrees, So angles A and C must be less than 90 degrees since a triangle's angles always must equal 180 degrees in total. Now that we know that B is 90 degrees, we can find x by dividing 90 by 3.
3x = 90
90/3 = 30
x = 30
Check:
3(30) = 90
We now know that x equals 30, so plug x into the other angles to find out what those ones equal. In this case, A equals 30, and C equals 2(30) = 60.
The measure of angle KJL is another way of asking for the measure of angle J since it is in the middle; it is where the angle is made. We know that the outside ∠JLM is 140 degrees, and ∠JKL is 75 degrees, so this makes the outside of ∠L = 140 degrees and ∠K = 75 degrees. If you remember our supplementary angles from above, this is almost the same concept. We see that JLM is a supplementary angle, and since it is 140 degrees this makes the inside of angle L equal to 40 (180 - 140 = 40.)
Now let's gather what we figured out: ∠K = 75 degrees and ∠L = 40 degrees. Remember that a triangle must always equal 180 degrees total, so add angles K and L together, then subtract that from 180.
180 - (75 + 40) = ∠J (which is another way of saying ∠KJL.)
180 - 115 = ∠J
65 = ∠J
Angle KJL is 65 degrees.
I know this is a lot of reading, so I am sorry if I made it a bit confusing. If you have anymore questions, feel free to ask! Hope this was helpful!
