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Q20.

Expert-verified
Found in: Page 696

### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776

# Find the measures of the numbered angles in the diagram.

The measure of the numbered angles is $m\angle 1=100°$, $m\angle 2=80°$, $m\angle 3=100°$, and $m\angle 4=80°$.

See the step by step solution

## Step 1. Given Information.

The provided figure is

Two angles are provided having the measure $80°$ and $80°$Step 2. Definition of consecutive interior angles..

## 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 1.

The sum of the linear paired angles is $180°$, $80°+m\angle 1=180°$.

The measure of $\angle 1$ will be,

$\begin{array}{c}{80}^{\circ }+m\angle 1={180}^{\circ }\\ \text{}m\angle 1={180}^{\circ }-{80}^{\circ }\\ \text{}m\angle 1={100}^{\circ }\end{array}$

## Step 4. Find the measure of angle 3.

The sum of the linear paired angles is$180°$, $80°+m\angle 3=180°$.

The measure of $\angle 3$ will be,

$\begin{array}{c}{80}^{\circ }+m\angle 3={180}^{\circ }\\ \text{}m\angle 3={180}^{\circ }-{80}^{\circ }\\ \text{}m\angle 3={100}^{\circ }\end{array}$

## Step 5. Find the measure of angle 4.

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

The measure of $\angle 4$ will be,

$\begin{array}{c}m\angle 4+m\angle 1={180}^{\circ }\\ m\angle 4={180}^{\circ }-m\angle 1\\ \text{}m\angle 4={180}^{\circ }-{100}^{\circ }\\ \text{}m\angle 4={80}^{\circ }\end{array}$

## Step 6. Find the measure of angle 2.

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

The measure of $\angle 2$ will be,

$\begin{array}{c}m\angle 2+m\angle 3={180}^{\circ }\\ \text{}m\angle 2={180}^{\circ }-m\angle 3\\ m\angle 2={180}^{\circ }-{100}^{\circ }\\ \text{}m\angle 2={80}^{\circ }\end{array}$

## Step 7. Conclusion.

The measure of the numbered angles is $m\angle 1=100°$, $m\angle 2=80°$, $m\angle 3=100°$ and $m\angle 4=80°$.