Chapter 3: Q7. (page 111)

In the diagram above $r ∥ s$ .
Solve for $y$ : $m ∠ 3 = 8 y - 40$ and $m ∠ 8 = 2 y + 20$ .

Short Answer

Expert verified

The value of $y$ is 20.

Step by step solution

Step 1. Highlight ∠3 and ∠8 in the given diagram.

Step 2. Apply the property of parallel lines.

If two parallel lines are intersected by a transversal then the same side interior angles are supplementary.

Step 3. Description of step.

From the given figure it can be observed that $r ∥ s$ and $t$ is transversal then by the definition of same side interior angles, $∠ 3$ and $∠ 8$ are same side interior angles and by property of parallel lines, $m ∠ 3 + m ∠ 8 = 180$ .

Step 4. Description of step.

Substitute $8 y - 40$ for $m ∠ 3$ and $2 y + 20$ for $m ∠ 8$ into $m ∠ 3 + m ∠ 8 = 180$ and simplify to obtain the value of y.

$\begin{array}{r} 8 y - 40 + 2 y + 20 = 180 \\ 10 y - 20 = 180 \\ 10 y = 200 \\ y = 20 \end{array}$

Therefore, the value of $y$ is 20.

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In the diagram above $r ∥ s$ .
Solve for $y$ : $m ∠ 3 = 8 y - 40$ and $m ∠ 8 = 2 y + 20$ .

Short Answer

Step by step solution

Step 1. Highlight ∠3 and ∠8 in the given diagram.

Step 2. Apply the property of parallel lines.

Step 3. Description of step.

Step 4. Description of step.

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In the diagram abover∥s.Solve for y:m∠3=8y-40 andm∠8=2y+20.

Short Answer

Step by step solution

Step 1. Highlight ∠3 and ∠8 in the given diagram.

Step 2. Apply the property of parallel lines.

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

Probability and Statistics

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Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

In the diagram above $r ∥ s$ .
Solve for $y$ : $m ∠ 3 = 8 y - 40$ and $m ∠ 8 = 2 y + 20$ .