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Katena32 [7]
3 years ago
5

Find the value of x and y

Mathematics
1 answer:
kotykmax [81]3 years ago
3 0

Answer:

x = 8

y = 29

Step-by-step explanation:

By verticle angles theorem, the angles with the measure of ( 4x + 17 ), and the angles with the measure of ( y + 20 ) are equal.

Verticles angles theorem states, when two lines intersect, there are four angles formed. The angles opposite to each other will have the same measure or congruent measures.

Hence one can say that;

4x + 17 = y + 20

Inverse operations;

4x + 17 = y + 20

     -17          -17

4x = y + 3

-3      -3

4x - 3 = y

Assuming that lines "m" and "n" are parallel, then the angles with the measure of ( 5x + 9 ) and the angles with the measure of ( y + 20 ) are congruent.

When two lines are parallel and are intersected by another line (transversal line), then the angles that are alternate and interior are congruent, in other words,  the same measure.

Based on that, one can say;

5x + 9 = y + 20

Earlier it was found that;

y = 4x - 3

Now substitute that into the previous equation, and solve using simplification and inverse operations;

5x + 9 = 4x - 3 + 20

5x + 9 = 4x + 17

     -9          -9

5x = 4x + 8

-4x   -4x

x = 8

Back solve to find y

y = 4x - 3

y = 4(8) - 3

y = 32 - 3

y = 29

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3 years ago
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erica [24]

Answer:

The measure of angle T is 135 degrees.

Step-by-step explanation:

Let's just say the measure of angles T and S are variables t and s.

So the equation would be...

t + s = 180

Since they are supplementary angles, they add up to 180.

Also, we know that t is 3 times s.

t = 3s

Now we can solve this system of equations.

Substitute 3s into t of the first equation.

3s + s = 180

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