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Q19.

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 $m\angle 1=90\xb0$, $m\angle 2=115\xb0$, and $m\angle 3=65\xb0$.

The provided figure is

The provided angle has the measure $115\xb0$.

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 $180\xb0$, $115\xb0+m\angle 3=180\xb0$.

The measure of $\angle 3$ will be,

$\begin{array}{c}{115}^{\circ}+m\angle 3={180}^{\circ}\\ \text{}m\angle 3={180}^{\circ}-{115}^{\circ}\\ \text{}m\angle 3={65}^{\circ}\end{array}$

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

The measure of $\angle 1$ will be,

$\begin{array}{c}{90}^{\circ}+m\angle 1={180}^{\circ}\\ \text{}m\angle 1={180}^{\circ}-{90}^{\circ}\\ \text{}m\angle 1={90}^{\circ}\end{array}$

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

The measure of $\angle 2$ will be,

$\begin{array}{c}m\angle 2+m\angle 3={180}^{\circ}\\ \text{}m\angle 2={180}^{\circ}-m\angle 3\\ m\angle 2={180}^{\circ}-{65}^{\circ}\\ \text{}m\angle 2={115}^{\circ}\end{array}$

The measure of the numbered angles is $m\angle 1=90\xb0$, $m\angle 2=115\xb0$, and $m\angle 3=65\xb0$.

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