Chapter 3: Q5 (page 80)

Assume that $a ∥ b$ and $c ∥ d$ .
If $m ∠ 13 = 110$ , then $m ∠ 15 = \underline{?}$ and $m ∠ 3 = \underline{?}$

Short Answer

Expert verified

Measurement of angles are: $m ∠ 15 = 110, and m ∠ 3 = 70$

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 15

$∠ 15$ is corresponding angle to $∠ 13$

Postulate 10: If two parallel lines are cut by a transversal then the corresponding angles are congruent

$\begin{matrix} ∠ 15 ≅ ∠ 13 \\ m ∠ 15 = m ∠ 13 \end{matrix}$

Thus, $m ∠ 15 = 110$

Step 3. Find m angle 11

$∠ 11$ forms a linear pair with $∠ 15$ , so sum of measurement of these two angles is 180

role="math" localid="1637671933532" $\begin{matrix} m ∠ 11 + m ∠ 15 = 180 \\ m ∠ 11 + 110 = 180 \end{matrix}$

role="math" localid="1637671993754" $\begin{matrix} m ∠ 11 = 180 - 110 \\ m ∠ 11 = 70 \end{matrix}$

Step 4. Find m angle 3

$∠ 3$ is a corresponding angle to $∠ 11$

Postulate 10: If two parallel lines are cut by a transversal then the corresponding angles are congruent

$\begin{matrix} ∠ 3 ≅ ∠ 11 \\ m ∠ 3 = m ∠ 11 \end{matrix}$

Thus, $m ∠ 3 = 70$

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Assume that $a ∥ b$ and $c ∥ d$ .
If $m ∠ 13 = 110$ , then $m ∠ 15 = \underline{?}$ and $m ∠ 3 = \underline{?}$

Short Answer

Step by step solution

Step 1. Observations from figure

Step 2. Find m angle 15

Step 3. Find m angle 11

Step 4. Find m angle 3

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Assume that a∥band c∥d.If m∠13=110, then m∠15=?¯and m∠3=?¯

Short Answer

Step by step solution

Step 1. Observations from figure

Step 2. Find m angle 15

Step 3. Find m angle 11

Step 4. Find m angle 3

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Mechanics Maths

Calculus

Probability and Statistics

Decision Maths

Study anywhere. Anytime. Across all devices.

Assume that $a ∥ b$ and $c ∥ d$ .
If $m ∠ 13 = 110$ , then $m ∠ 15 = \underline{?}$ and $m ∠ 3 = \underline{?}$