Chapter 5: Q27 (page 170)

$▱ DECK$ is a parallelogram. Complete.
If $m ∠ 1 = 3 x, m ∠ 2 = 4 x$ and $m ∠ 3 = x^{2} - 70$ then $x = ?$ and $m ∠ CED = ?$ (numerical answers).

Short Answer

Expert verified

The value of x and $∠ C E D$ is 10 and $70 °$ respectively.

Step by step solution

Step 1. Apply property of parallelogram.

Alternate interior angles of a parallelogram are equal.

From the figure, it can be observed that,

$\begin{matrix} 3 x = x^{2} - 70 \\ x^{2} - 3 x - 70 = 0; \\ 4 x = ∠ D E K \end{matrix}$

Step 2. Description of step.

Solve the obtained quadratic equation in step 1 to find the value of x.

$\begin{array}{l} x^{2} - 3 x - 70 = 0 \\ x^{2} - 10 x + 7 x - 70 = 0 \\ x (x - 10) + 7 (x - 10) = 0 \\ x - 10 = 0 or x + 7 = 0 \\ x = 10 orx = - 7 \end{array}$

Step 3. Solve the quadratic equation.

Solving equation $x^{2} - 3 x - 70 = 0$ gives the roots as, $x = 10; x = - 7$

Only positive values are to be considered, therefore the acceptable value of x is 10.

Step 4. Solve the quadratic equation.

$∠ C E D$ can be expressed as $∠ C E D = ∠ D E K + x^{2} - 70$ .

Substitute 4x for $∠ D E K$ into $∠ C E D = ∠ D E K + x^{2} - 70$ .

$∠ C E D = 4 x + x^{2} - 70$

Step 5. Description of step.

Substitute 10 for x into $∠ C E D = 4 x + x^{2} - 70$ .

$\begin{matrix} ∠ C E D = 4 (10) + {(10)}^{2} - 70 \\ = 40 + 100 - 70 \\ = 70 ° \end{matrix}$

Therefore, the value of x and $∠ C E D$ is 10 and $70 °$ respectively.

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$▱ DECK$ is a parallelogram. Complete.
If $m ∠ 1 = 3 x, m ∠ 2 = 4 x$ and $m ∠ 3 = x^{2} - 70$ then $x = ?$ and $m ∠ CED = ?$ (numerical answers).

Short Answer

Step by step solution

Step 1. Apply property of parallelogram.

Step 2. Description of step.

Step 3. Solve the quadratic equation.

Step 4. Solve the quadratic equation.

Step 5. Description of step.

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▱DECKis a parallelogram. Complete.Ifm∠1=3x,m∠2=4x and m∠3=x2-70then x=?andm∠CED=? (numerical answers).

Short Answer

Step by step solution

Step 1. Apply property of parallelogram.

Step 2. Description of step.

Step 3. Solve the quadratic equation.

Step 4. Solve the quadratic equation.

Step 5. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Applied Mathematics

Theoretical and Mathematical Physics

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

$▱ DECK$ is a parallelogram. Complete.
If $m ∠ 1 = 3 x, m ∠ 2 = 4 x$ and $m ∠ 3 = x^{2} - 70$ then $x = ?$ and $m ∠ CED = ?$ (numerical answers).