In the figure, m∠L1 = (5x)°, m∠L2 = (4x + 10)° and, m∠L3 = (10x – 5)°. What is m∠L3, in degrees?

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)