Chapter 10: Q.22 (page 545)

For the trapezoid shown, the ratio $m ∠ A : m ∠ C$ is $2 : 1$ . Write and solve an equation to find the value of x.

Short Answer

Expert verified

The value of x is $60 °$ .

Step by step solution

Step 1. Given Information.

The ratio $m ∠ A : m ∠ C$ is $2 : 1$ . The figure is shown below.

Step 2. Concept Used.

Angle sum property of quadrilateral.

$∠ A + ∠ B + ∠ C + ∠ D = 360 °$

Step 3. Calculation.

From the figure,

$\begin{array}{l} ∠ D = ∠ C \\ ∠ A = ∠ B \end{array}$

$∠ C = x °$

And,

$∠ A : ∠ C = 2 : 1$

So,

$\begin{array}{l} ∠ A = 2 x^{°} \\ ∠ B = 2 x^{°} \end{array}$

According to angle sum properties of quadrilateral,

$∠ A + ∠ B + ∠ D + ∠ C = 360 °$

Substituting the value of angles,

$\begin{array}{l} 2 x + 2 x + x + x = 360^{°} \\ 6 x = 360^{°} \\ x = 60^{°} \end{array}$

Step 4. Conclusion.

The value of x is $60 °$ .

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For the trapezoid shown, the ratio $m ∠ A : m ∠ C$ is $2 : 1$ . Write and solve an equation to find the value of x.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Concept Used.

Step 3. Calculation.

Step 4. Conclusion.

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For the trapezoid shown, the ratio m∠A:m∠C is2:1. Write and solve an equation to find the value of x.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Concept Used.

Step 3. Calculation.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Logic and Functions

Statistics

Pure Maths

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

For the trapezoid shown, the ratio $m ∠ A : m ∠ C$ is $2 : 1$ . Write and solve an equation to find the value of x.