Chapter 3: Q6 (page 80)

Assume that $a ∥ b$ and $c ∥ d$ .
If $m ∠ 7 = x$ , then $m ∠ 12 = \underline{?}$ and $m ∠ 6 = \underline{?}$

Short Answer

Expert verified

Measurement of angles are: $m ∠ 12 = x, and m ∠ 6 = 180 - x$

Step by step solution

Step 1. Observations from figure

$a$ is transversal to parallel lines $c$ and $d$
$b$ is transversal to parallel lines $c$ and $d$
$c$ is transversal to parallel lines $a$ and $b$
$d$ is transversal to parallel lines $a$ and $b$

Step 2. Find m angle 12

$∠ 7 and ∠ 12$ forms a pair of alternate interior angles Theorem 3-2: If two parallel lines are cut by a transversal then the alternate interior angles are congruent.

$\begin{matrix} ∠ 12 ≅ ∠ 7 \\ m ∠ 12 = m ∠ 7 \end{matrix}$

Thus, $m ∠ 12 = x$

Step 3. Find m angle 6

$∠ 7 and ∠ 12$ forms a pair of same-side interior angles Theorem 3-3: If two parallel lines are cut by a transversal then the same-side interior angles are supplementary.

role="math" localid="1637740498726" $\begin{matrix} m ∠ 6 + m ∠ 7 = 180 \\ m ∠ 6 + x = 180 \\ m ∠ 6 = 180 - x \end{matrix}$

Thus, $m ∠ 6 = 180 - x$

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Statement	Reason
1. $k ∥ l$	Given
2. $∠ 3 ≅ ∠ 2$	If two parallel lines are cut by transversal then alt. int. $∠ s$ are $≅$
3. $∠ 1 ≅ ∠ 3$	Vert. $∠ s$ are $≅$
4. $∠ 1 ≅ ∠ 2$	Transitive Property

Assume that $a ∥ b$ and $c ∥ d$ .
If $m ∠ 7 = x$ , then $m ∠ 12 = \underline{?}$ and $m ∠ 6 = \underline{?}$

Short Answer

Step by step solution

Step 1. Observations from figure

Step 2. Find m angle 12

Step 3. Find m angle 6

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Assume that a∥band c∥d.If m∠7=x, then m∠12=?¯and m∠6=?¯

Short Answer

Step by step solution

Step 1. Observations from figure

Step 2. Find m angle 12

Step 3. Find m angle 6

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

Mechanics Maths

Logic and Functions

Theoretical and Mathematical Physics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Assume that $a ∥ b$ and $c ∥ d$ .
If $m ∠ 7 = x$ , then $m ∠ 12 = \underline{?}$ and $m ∠ 6 = \underline{?}$