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Find the values of x and y in the diagram below.
(4x-7)
86°
(7y-1)⁰
(9x + 4)

Find The Values Of X And Y In The Diagram Below 4x7 86 7y1 9x 4 class=

Sagot :

Acyclicsidn

Answer:

x = 15 and y = 6

Step-by-step explanation:

First we must find x to find y

We can find x using the exterior angle of a triangle statement

Statement : the exterior angle of a triangle is equal to the opposite interior angles (see attached image)

This means that 9x + 4 = 86 + 4x - 7

9x + 4 = 86 + 4x - 7  

==> combine like terms

9x + 4 = 79 + 4x

==> subtract 4 from both sides

9x = 75 + 4x

==> subtract 4x from both sides

5x = 75

==> divide both sides by 75

x = 15

Now we plug in the value of x into the interior angle of the triangle so we can use the angles in a triangle theorem which states that the angles of a triangle add up to 180 degrees

So we have 86 + 4x - 7 + 7y - 1 = 180

86 + 4x - 7 + 7y - 1 = 180

==> plug in x = 15

86 + 4(15) - 7 + 7y - 1 = 180

==> multiply 4 and 15

86 + 60 - 7 + 7y - 1 = 180

==> combine like terms

138 + 7y = 180

==> subtract 138 from both sides

7y = 42

==> divide both sides by 7

y = 6

So we know x = 15 and y = 6

View image Acyclics

Answer:

x = 15

y = -6

Step-by-step explanation:

The outside angle equals the measurement of the two angles farthest from it.

86 + 4x -7 = 9x + 4  Combine like terms

79 + 4x = 9x + 4  Subtract 4x from both sides

79 = 5x + 4  Subtract 4 from both sides

75 = 5x  Divide both sides by 5

15 = x

The sum of the interior angels of a triangle is 180

86 + 4x -7 + 7y - 1 = 180  Substitute in 15 for x

86 + (4)(15) -7 + 7y -1 = 180

86 +60 -7 +7y -1 = 180  Combine like terms

138 +7y = 180  Subtract 138 from both sides

7y = 42  Divide both sides by 7

y = -6

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