## 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)

Question

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

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