Chapter 5: Q28 (page 170)

$▱ DECK$ is a parallelogram. Complete.
If $m ∠ 1 = 42, m ∠ 2 = x^{2}$ and $m ∠ CED = 13 x$ then $m ∠ 2 = ?$ or $m ∠ 2 = ?$ (numerical answers).

Short Answer

Expert verified

The value of $m ∠ 2$ is $36 °$ or $49 °$ .

Step by step solution

Step 1. Apply property of parallelogram.

The opposite angles of a parallelogram are congruent.

From the given figure, it can be observed that $∠ K$ and $∠ E$ are opposite angles, such that,

$\begin{matrix} m ∠ 1 + m ∠ 2 = m ∠ C E D \\ 42 + x^{2} = 13 x \\ x^{2} - 13 x + 42 = 0 \end{matrix}$

Step 2. Solve the quadratic equation.

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

$\begin{array}{l} x^{2} - 13 x + 42 = 0 \\ x^{2} - 6 x - 7 x + 42 = 0 \\ x (x - 6) - 7 (x - 6) = 0 \\ x - 6 = 0 or x - 7 = 0 \\ x = 6 orx = 7 \end{array}$

Solving equation $x^{2} - 3 x - 70 = 0$ gives the roots as, $x = 6 or x = 7$ .

Step 3. Description of step.

Substitute 6 for x into $m ∠ 2 = x^{2}$ to find the value of $m ∠ 2$ .

$\begin{matrix} m ∠ 2 = x^{2} \\ = 6^{2} \\ = 36 ° \end{matrix}$

Step 4. Description of step.

Substitute 7 for x into $m ∠ 2 = x^{2}$ to find the value of $m ∠ 2$ .

$\begin{matrix} m ∠ 2 = x^{2} \\ = 7^{2} \\ = 49 ° \end{matrix}$

Therefore, the value of $m ∠ 2$ is $36 °$ or $49 °$ .

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$▱ DECK$ is a parallelogram. Complete.
If $m ∠ 1 = 42, m ∠ 2 = x^{2}$ and $m ∠ CED = 13 x$ then $m ∠ 2 = ?$ or $m ∠ 2 = ?$ (numerical answers).

Short Answer

Step by step solution

Step 1. Apply property of parallelogram.

Step 2. Solve the quadratic equation.

Step 3. Description of step.

Step 4. Description of step.

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▱DECKis a parallelogram. Complete.If m∠1=42,m∠2=x2and m∠CED=13xthen m∠2=?or m∠2=?(numerical answers).

Short Answer

Step by step solution

Step 1. Apply property of parallelogram.

Step 2. Solve the quadratic equation.

Step 3. Description of step.

Step 4. Description of step.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Statistics

Mechanics Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Geometry

Study anywhere. Anytime. Across all devices.

$▱ DECK$ is a parallelogram. Complete.
If $m ∠ 1 = 42, m ∠ 2 = x^{2}$ and $m ∠ CED = 13 x$ then $m ∠ 2 = ?$ or $m ∠ 2 = ?$ (numerical answers).