A fence on a hill uses vertical posts L and M to hold parallel rails N and P. If m∠1 = 115, then what is the measure of ∠16?
1 answer:
Step-by-step explanation:
Given information:
A fence on a hill uses vertical posts L and M to hold parallel rails N and P
The diagram is attached below
Here lines N and P are parallel lines
Transversal line for parallel lines N and P is line L
Calculation:
angle 1 and angle 16 are consecutive exterior angles
If parallel lines are cut by a transversal then consecutive exterior angles are supplementary
So measurement of angle 16 = 65 degrees
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Solution:
LCD for 5 and 5x is 5x
←cross product
20x + 30 = 5x² + 25x ←simplify with distributive property
0 = 5x² + 5x - 30 ←use inverse operations to collect all terms on one side
0 = x² + x - 6 ←if possible divide by numerical GCF (This case 5)
0 = (x + 3)(x - 2) ←Factor
x = -3 or x = 2
Please check by substitution in original equation... Both work
Solution:
LCD for 5 and 5x is 5x
20x + 30 = 5x² + 25x ←simplify with distributive property
0 = 5x² + 5x - 30 ←use inverse operations to collect all terms on one side
0 = x² + x - 6 ←if possible divide by numerical GCF (This case 5)
0 = (x + 3)(x - 2) ←Factor
x = -3 or x = 2
Please check by substitution in original equation... Both work