Chapter 4: Q28. (page 139)

Find the values of x and y.
In equilateral $Δ D E F,$ $m ∠ D = x + y$ and $m ∠ E = 2 x - y$ .

Short Answer

Expert verified

The value of $x$ and $y$ is 40and 20 respectively.

Step by step solution

Step 1. Apply definition of equilateral triangle.

An equilateral triangle is a triangle which all the three angles are equal in length, that is, $60 °$ .

Therefore, in $Δ D E F$ , $m ∠ D = m ∠ E = m ∠ F = 60$ .

Step 2. Description of step.

Consider, $m ∠ D = 60$ .

Substitute $x + y$ for $m ∠ D$ into $m ∠ D = 60$ and simplify.

$x + y = 60$

Step 3. Description of step.

Consider, $m ∠ E = 60$ .

Substitute $2 x - y$ for $m ∠ E$ into $m ∠ E = 60$ and simplify.

$2 x - y = 60$

Step 4. Description of step.

Add $x + y = 60$ and $2 x - y = 60$ , to find the value of $x$ .

$x + y + 2 x - y = 60 + 60 3 x = 120 x = 40$

Step 5. Description of step.

Substitute 40 for $x$ into $x + y = 60$ , to find the value of $y$ .

$40 + y = 60 y = 60 - 40 = 20$

Therefore, the value of $x$ and $y$ is 40 and 20 respectively.

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Find the values of x and y.
In equilateral $Δ D E F,$ $m ∠ D = x + y$ and $m ∠ E = 2 x - y$ .

Short Answer

Step by step solution

Step 1. Apply definition of equilateral triangle.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Description of step.

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Find the values of x and y.In equilateralΔDEF,m∠D=x+y and m∠E=2x-y.

Short Answer

Step by step solution

Step 1. Apply definition of equilateral triangle.

Step 2. Description of step.

Step 3. Description of step.

Step 4. Description of step.

Step 5. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Find the values of x and y.
In equilateral $Δ D E F,$ $m ∠ D = x + y$ and $m ∠ E = 2 x - y$ .