Book edition Common Core Edition

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

Pages 183 pages

ISBN 9780547587776

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Short Answer

Find the measures of the numbered angles in the diagram.

The measure of the numbered angles is $m ∠ 1 = 90 °$ , $m ∠ 2 = 115 °$ , and $m ∠ 3 = 65 °$ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

The provided figure is

The provided angle has the measure $115 °$ .

Step 2. Definition of consecutive interior angles.

When two lines are crossed by another line, it is known as transversal. The angles internal to the two parallel lines, on the same side of the transversal are called consecutive interior angles. The sum of two consecutive interior angles is $180 °$ .

Step 3. Find the measure of angle 3.

The sum of the linear paired angles is $180 °$ , $115 ° + m ∠ 3 = 180 °$ .

The measure of $∠ 3$ will be,

$\begin{matrix} 115^{\circ} + m ∠ 3 = 180^{\circ} \\ m ∠ 3 = 180^{\circ} - 115^{\circ} \\ m ∠ 3 = 65^{\circ} \end{matrix}$

Step 4. Find the measure of angle 1.

The sum of consecutive interior angles is $180 °$ .

The measure of $∠ 1$ will be,

$\begin{matrix} 90^{\circ} + m ∠ 1 = 180^{\circ} \\ m ∠ 1 = 180^{\circ} - 90^{\circ} \\ m ∠ 1 = 90^{\circ} \end{matrix}$

Step 5. Find the measure of angle 2.

The sum of consecutive interior angles is\[180{}^\circ \].

The measure of $∠ 2$ will be,

$\begin{matrix} m ∠ 2 + m ∠ 3 = 180^{\circ} \\ m ∠ 2 = 180^{\circ} - m ∠ 3 \\ m ∠ 2 = 180^{\circ} - 65^{\circ} \\ m ∠ 2 = 115^{\circ} \end{matrix}$

Step 6. Conclusion.

The measure of the numbered angles is $m ∠ 1 = 90 °$ , $m ∠ 2 = 115 °$ , and $m ∠ 3 = 65 °$ .

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Pre-algebra

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Short Answer

Find the measures of the numbered angles in the diagram.

Step by Step Solution

Step 1. Given Information.

Step 2. Definition of consecutive interior angles.

Step 3. Find the measure of angle 3.

Step 4. Find the measure of angle 1.

Step 5. Find the measure of angle 2.

Step 6. Conclusion.

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Pre-algebra

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Short Answer

Find the measures of the numbered angles in the diagram.

Step by Step Solution

Step 1. Given Information.

Step 2. Definition of consecutive interior angles.

Step 3. Find the measure of angle 3.

Step 4. Find the measure of angle 1.

Step 5. Find the measure of angle 2.

Step 6. Conclusion.

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