Mathematics

Question

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. (4x-7) 86° (7y-1)⁰ (9x + 4)

2 Answer

  • 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

  • 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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