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2 years ago

I need an answer soon, please! Whoever answers first will get Brainliest!!! Please no troll answers!

Mathematics

2 answers:

Colt1911 [192]2 years ago

8 0

Answer:

x = 8, and y = 12

Step-by-step explanation:

There are 2 variables, so you need 2 equations to form a system of equations in two variables.

The upper left triangle has all angle measures given: 100, 2x + y, 5x + y. We know that the sum of the measures of the angles of a triangle is 180.

First equation:

100 + 2x + y + 5x + y = 180

Simplify:

7x + 2y = 80 (First equation)

Now we see that the upper and lower sides are parallel, so alternate interior angles are congruent. The angles measuring 2x + y and 5x - y are alternate interior angles and are congruent.

Second equation:

2x + y = 5x - y

Simplify:

3x - 2y = 0 (Second equation)

Now we use the first equation and the second equation as a system of simultaneous equations to solve for x and y.

7x + 2y = 80

3x - 2y = 0

Solve the second equation for 2x.

3x = 2y

Now replace 2y in the first equation with 3x.

7x + 3x = 80

10x = 80

x = 8

Replace x with 8 in the second equation.

3(8) - 2x = 0

24 = 2x

x = 12

Answer: x = 8, and y = 12

Readme [11.4K]2 years ago

7 0

Answer:

x= 8
y = 12

Step-by-step explanation:

Alternate interior angles are equal

Therefore 5x - y = 2x + y

5x - 2x - y = 2x - 2x + y

3x - y = y

3x = 2y

All triangles have 180

Solve for x

100 + 5x + y +2x + y = 180
100 + 7x + 2y = 180
7x + 2y = 180 - 100
7x + 2y = 80 Substitute 3x for 2y
7x + 3x = 80
10x = 80
x = 8

Solve for y

7x + 2y = 80
7*8 + 2y = 80
56 + 2y = 80
2y = 24
y = 12

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