In the figure, m∠L1 = (5x)°, m∠L2 = (4x + 10)° and, m∠L3 = (10x – 5)°. What is m∠L3, in degrees?
A) 35
B) 40
C) 45
D) 50
In the figure, m∠L1 = (5x)°, m∠L2 = (4x + 10)° and, m∠L3 = (10x – 5)°. What is m∠L3, in degrees?
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In the figure, m∠L1 = (5x)°, m∠L2 = (4x + 10)° and, m∠L3 = (10x – 5)°. What is m∠L3, in degrees?
A) 35
B) 40
C) 45
D) 50
To find ( m∠L3 ), we first need to express the relationship between the angles. Assuming ( ∠L1 ), ( ∠L2 ), and ( ∠L3 ) are angles in a triangle (which typically sum to 180°), we can set up the equation:
[
m∠L1 + m∠L2 + m∠L3 = 180°
]
Substituting the given expressions:
[
(5x) + (4x + 10) + (10x – 5) = 180
]
Now, combine like terms:
[
5x + 4x + 10 + 10x – 5 = 180
]
[
(5x + 4x + 10x) + (10 – 5) = 180
]
[
19x + 5 = 180
]
Next, isolate ( x ):
[
19x = 180 – 5
]
[
19x = 175
]
[
x = frac{175}{19} approx 9.21
]
Now substitute ( x ) back to find ( m∠L3 ):
[
m∠L3 = 10x – 5
]
[
m∠L3 = 10 left(frac{175}{19}right)