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Digiron [165]
3 years ago
14

What is the value of x which proves that the runways are parallel? What is the measure of the larger angle?

Mathematics
1 answer:
makkiz [27]3 years ago
6 0

Answer:

118°

Step-by-step explanation:

When two parallel lines are cut by a tranversal, then the exterior angles are supplimentary and the corresponding angles are congruent.

Therefore the angle above (15x - 17)° is also (5x + 17)° and the angle below (5x + 17)° is also (15x - 17)°.

Angles on a straight line adds up to 180°. So to know the measure of the larger angle we must both equations and equal it to 180° to find x in order to know the larger angle.

(5x + 17) + (15x - 17) = 180

5x + 15x + 17 - 17 = 180

20x = 180

20x/20 = 180/20

x = 9°

Nkw let's substitute x = 9 into the equations

5x + 17 =

5(9) + 17 =

= 62°

15x - 17 =

15(9) - 17 =

= 118°

Both equations should add up to be 180°.

Therefore the measure of the largest angle is 118°.

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Step-by-step explanation:

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(A) Let's solve for "y" from the first equation:

3x-2y=-1\\\\-2y=-3x-1\\\\y=\frac{3}{2}x+\frac{1}{2}

You can notice that:

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Substituting those values into the second equation and solving for "y", you get:

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You can idenfity that:

m=\frac{3}{2}\\\\c=-\frac{1}{2}

Therefore, they are parallel.

(B) In order make that the System has Infinite solutions, the slopes and the y-intercepts of both equations must be the same. Then, the values of "a" and "b" can be:

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6x+(-4y)=-2\\\\-4y=-6x-2\\\\y=\frac{-6}{-4}x-\frac{2}{-4}\\\\y=\frac{3}{2}x+\frac{1}{2}

You can identify that:

m=\frac{3}{2}\\\\b=\frac{1}{2}

Therefore, they are the same line.

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