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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)
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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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Mathematics
6 months
2021-07-22T15:25:45+00:00
2021-07-22T15:25:45+00:00 1 Answers
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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