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Expert-verified Found in: Page 689 ### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776 # In the diagram shown, $m\angle 1=35°$ and $m\angle 3=110°$. What is $m\angle 5$? Tell how $\angle 1$ and $\angle 2$ are related. Then find $m\angle 2$.Tell how $\angle 3$ and $\angle 4$ are related. Then find $m\angle 4$.Use what you know about the sum of the measures of the angles of a triangle to find $m\angle 5$.

1. The measure of angle $m\angle 2$ is $35°$.

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

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

See the step by step solution

## Step 1. Given Information.

The measures $m\angle 1=35°$ and $m\angle 3=110°$ 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, $\angle 1$ and $\angle 2$are vertical angles. So,

$m\angle 2=m\angle 1$

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

$m\angle 2=35°$

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

$m\angle 3+m\angle 4=180°$

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

$\begin{array}{c}m\angle 4+110°=180°\\ m\angle 4=70°\end{array}$

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

$m\angle 2+m\angle 4+m\angle 5=180°$

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

$\begin{array}{c}m\angle 5+70°+35°=180°\\ m\angle 5=180°-\left(35°+70°\right)\\ =180°-105°\\ =75°\end{array}$ ### Want to see more solutions like these? 