Book edition Common Core Edition

Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

Pages 183 pages

ISBN 9780547587776

Answers without the blur.

Just sign up for free and you're in.

Short Answer

In the diagram shown, $m ∠ 1 = 35 °$ and $m ∠ 3 = 110 °$ . What is $m ∠ 5$ ?
Tell how $∠ 1$ and $∠ 2$ are related. Then find $m ∠ 2$ .
Tell how $∠ 3$ and $∠ 4$ are related. Then find $m ∠ 4$ .
Use what you know about the sum of the measures of the angles of a triangle to find $m ∠ 5$ .

The measure of angle $m ∠ 2$ is $35 °$ .

2. The measure of angle $m ∠ 4$ is $70 °$ .

3. The measure of angle $m ∠ 5$ is $75 °$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

The measures $m ∠ 1 = 35 °$ and $m ∠ 3 = 110 °$ in the following figure.

Step 2. Concept used.

The measures of a pair of vertical angles are equal.
The sum of measures of a pair of adjacent angles forming a straight angle (supplementary angles) is $180 °$ .
The sum of the measures of the three angles of a triangle is $180 °$ .

Step 3. Calculation.

In the given figure, $∠ 1$ and $∠ 2$ are vertical angles. So,

$m ∠ 2 = m ∠ 1$

Put the given value of $m ∠ 1 = 35 °$ in the above equation to write

$m ∠ 2 = 35 °$

Now, in the figure, $∠ 3$ and $∠ 4$ are supplementary angles as they together form a straight angle. So,

$m ∠ 3 + m ∠ 4 = 180 °$

Put the given value of $m ∠ 3 = 110 °$ in the above equation to write,

$\begin{matrix} m ∠ 4 + 110 ° = 180 ° \\ m ∠ 4 = 70 ° \end{matrix}$

Finally, since in the figure c form a triangle, the sum of their measures should be equal to $180 °$ . So,

$m ∠ 2 + m ∠ 4 + m ∠ 5 = 180 °$

Put the earlier computed values of $m ∠ 2$ and $m ∠ 4$ in the above equation to write,

$\begin{matrix} m ∠ 5 + 70 ° + 35 ° = 180 ° \\ m ∠ 5 = 180 ° - (35 ° + 70 °) \\ = 180 ° - 105 ° \\ = 75 ° \end{matrix}$

Find Study Materials for

Create Study Materials

Select your language

Pre-algebra

Answers without the blur.

Short Answer

Step by Step Solution

Step 1. Given Information.

Step 2. Concept used.

Step 3. Calculation.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Select your language

Pre-algebra

Answers without the blur.

Short Answer

In the diagram shown, m∠1=35° and m∠3=110°. What is m∠5?Tell how ∠1 and ∠2 are related. Then find m∠2.Tell how ∠3 and ∠4 are related. Then find m∠4.Use what you know about the sum of the measures of the angles of a triangle to find m∠5.

Step by Step Solution

Step 1. Given Information.

Step 2. Concept used.

Step 3. Calculation.

Most popular questions for Math Textbooks

Want to see more solutions like these?

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Probability and Statistics

Statistics

Mechanics Maths

Geometry

Pure Maths