StudySmarter AI is coming soon!

- :00Days
- :00Hours
- :00Mins
- 00Seconds

A new era for learning is coming soonSign up for free

Suggested languages for you:

Americas

Europe

Q20.

Expert-verifiedFound in: Page 696

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 $m\angle 1=100\xb0$, $m\angle 2=80\xb0$, $m\angle 3=100\xb0$, and $m\angle 4=80\xb0$.

The provided figure is

Two angles are provided having the measure $80\xb0$ and $80\xb0$**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 $180\xb0$****.**

The sum of the linear paired angles is $180\xb0$, $80\xb0+m\angle 1=180\xb0$.

The measure of $\angle 1$ will be,

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

The sum of the linear paired angles is$180\xb0$, $80\xb0+m\angle 3=180\xb0$.

The measure of $\angle 3$ will be,

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

The sum of consecutive interior angles is $180\xb0$.

The measure of $\angle 4$ will be,

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

The sum of consecutive interior angles is $180\xb0$.

The measure of $\angle 2$ will be,

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

The measure of the numbered angles is $m\angle 1=100\xb0$, $m\angle 2=80\xb0$, $m\angle 3=100\xb0$ and $m\angle 4=80\xb0$.

94% of StudySmarter users get better grades.

Sign up for free