Given
\qquad m \angle LONm∠LONm, angle, L, O, N is a straight angle.
\qquad m \angle LOM = 4x + 30^\circm∠LOM=4x+30
∘
m, angle, L, O, M, equals, 4, x, plus, 30, degrees
\qquad m \angle MON = 8x + 90^\circm∠MON=8x+90
∘
m, angle, M, O, N, equals, 8, x, plus, 90, degrees
Find m\angle MONm∠MONm, angle, M, O, N:
girl idk ima update this when i check the answers
m∠LON=113
∘
m, angle, L, O, N, equals, 113, degrees
\qquad m \angle MON = 2x + 33^\circm∠MON=2x+33
∘
m, angle, M, O, N, equals, 2, x, plus, 33, degrees
\qquad m \angle LOM = 3x + 20^\circm∠LOM=3x+20
∘
m, angle, L, O, M, equals, 3, x, plus, 20, degrees
Find m\angle MONm∠MONm, angle, M, O, N:
To find the measure of angle MON (m∠MON), we can use the fact that the sum of the angles in a straight line is 180 degrees.
From the given information, we have:
m∠LON = 180 degrees (since LON is a straight angle)
We can also use the fact that angles LON, LOM, and MON form a straight line, so their measures add up to 180 degrees:
m∠LON + m∠LOM + m∠MON = 180 degrees
Substituting the given measures:
180 degrees + (4x + 30 degrees) + (8x + 90 degrees) = 180 degrees
Simplifying, we combine like terms:
4x + 30 degrees + 8x + 90 degrees = 0 degrees
12x + 120 degrees = 0 degrees
Now, isolate the variable:
12x = -120 degrees
Divide both sides by 12:
x = -120 degrees / 12 = -10 degrees
Substitute the value of x back into the expression for m∠MON:
m∠MON = 8x + 90 degrees
m∠MON = 8(-10 degrees) + 90 degrees
m∠MON = -80 degrees + 90 degrees
m∠MON = 10 degrees
Therefore, the measure of angle MON (m∠MON) is 10 degrees.