PLEASE HELP ∆JKL is an isosceles triangle with vertex angle K. Find the values of x and y if JK = 8x, KL = 13x – 15, m∠KJL=(5y-3)

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PLEASE HELP

∆JKL is an isosceles triangle with vertex angle K. Find the values of x and y if JK = 8x, KL = 13x – 15, m∠KJL=(5y-3)°, and m∠JKL=76°.

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Hồng Cúc 6 months 2021-07-22T15:25:45+00:00 1 Answers 9 views 0

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    2021-07-22T15:27:19+00:00

    Answer:

    The values of x and y are x = 3 and y = 11

    Step-by-step explanation:

    The isosceles triangle has two equal sides in length, and its base angles are equal in measures

    In ΔJKL

    ∵ ΔJKL is an isosceles triangle with vertex K

    → That means the equal sides are JK and KL

    JK = KL

    ∵ JK = 8x and KL = 13x – 15

    → Equate them

    13x – 15 = 8x

    → Add 15 to both sides

    ∵ 13x – 15 + 15 = 8x + 15

    ∴ 13x = 8x + 15

    → Subtract 8x from both sides

    ∵ 13x – 8x = 8x – 8x + 15

    ∴ 5x = 15

    → Divide both sides by 5 to find x

    x = 3

    ∵ K is the vertex of the ΔJKL

    ∴ ∠KJL and ∠KLJ are the base angles

    ∵ The base angles are equal in measures

    m∠KJL = m∠KLJ

    ∵ m∠KJL = 5y – 3

    ∴ m∠KLJ = 5y – 3

    ∵ The sum of the measures of the angles of a Δ is 180°

    m∠KJL + m∠KLJ + m∠JKL = 180°

    ∵ m∠JKL = 76°

    → Substitute the measures of the 3 angles in the equation

    5y – 3 + 5y – 3 + 76 = 180

    → Add the like terms on the left side

    ∵ (5y + 5y) + (76 – 3 – 3) = 180

    ∴10y + 70 =180

    → Subtract 70 from both sides

    ∵ 10y + 70 – 70 = 180 – 70

    ∴ 10y = 110

    → Divide both sides by 10 to find y

    y = 11

    The values of x and y are x = 3 and y = 11

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