Chapter 4: Q29. (page 139)

Find the values of x and y.
29. In $Δ JKL, \bar{JK} ≅ \bar{KL}, m ∠ J = 2 x - y, m ∠ K = 2 x + 2 y$ and $m ∠ L = x + 2 y$

Short Answer

Expert verified

The value of $x$ and $y$ is 30and 10 respectively.

Step by step solution

– Apply isosceles triangle theorem.

If the two sides of a triangle are congruent, then the angles opposite to those sides are congruent.

In $Δ J K L, \bar{J K} ≅ \bar{K L}$ implies that $m ∠ J = m ∠ L$ .

– Description of step.

Substitute $2 x - y$ for $m ∠ J$ and $x + 2 y$ for $m ∠ L$ into $m ∠ J = m ∠ L$ and simplify.

$\begin{array}{l} 2 x - y = x + 2 y \\ x = 3 y \end{array}$

– Apply an angle sum theorem.

The sum of measures of all interior angles of a triangle is 180.

Therefore,

$\begin{matrix} m ∠ J + m ∠ K + m ∠ L = 180 \\ 2 x - y + 2 x + 2 y + x + 2 y = 180 \\ 5 x + 3 y = 180 \end{matrix}$

– Description of step.

Substitute $3 y$ for $x$ into $5 x + 3 y = 180$ to find the value of role="math" localid="1648815869555" $x$ .

$\begin{matrix} 5 (3 y) + 3 y = 180 \\ 15 y + 3 y = 180 \\ 18 y = 180 \\ y = 10 \end{matrix}$

– Description of step.

Substitute 10 for $y$ into $x = 3 y$ , to find the value of $x$ .

$\begin{matrix} x = 3 \times 10 \\ = 30 \end{matrix}$

Therefore, the value of $x$ and $y$ is 30 and 10 respectively.

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Find the values of x and y.
29. In $Δ JKL, \bar{JK} ≅ \bar{KL}, m ∠ J = 2 x - y, m ∠ K = 2 x + 2 y$ and $m ∠ L = x + 2 y$

Short Answer

Step by step solution

– Apply isosceles triangle theorem.

– Description of step.

– Apply an angle sum theorem.

– Description of step.

– Description of step.

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Find the values of x and y.29. In ΔJKL,JK¯≅KL¯,m∠J=2x-y,m∠K=2x+2yandm∠L=x+2y

Short Answer

Step by step solution

– Apply isosceles triangle theorem.

– Description of step.

– Apply an angle sum theorem.

– Description of step.

– Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Statistics

Theoretical and Mathematical Physics

Applied Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Find the values of x and y.
29. In $Δ JKL, \bar{JK} ≅ \bar{KL}, m ∠ J = 2 x - y, m ∠ K = 2 x + 2 y$ and $m ∠ L = x + 2 y$