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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