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Q8.

Expert-verifiedFound in: Page 689

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, $m\angle 1=35\xb0$**** and $m\angle 3=110\xb0$. 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 $m\angle 5$.**

- The measure of angle $m\angle 2$ is $35\xb0$.

2. The measure of angle $m\angle 4$ is $70\xb0$.

3. The measure of angle $m\angle 5$ is$75\xb0$.

The measures $m\angle 1=35\xb0$ and $m\angle 3=110\xb0$ in the following figure.

- 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 $180\xb0$****.** - The
**sum of the measures of the three angles of a triangle is $180\xb0$**.

In the given figure, $\angle 1$ and $\angle 2$are vertical angles. So,

$m\angle 2=m\angle 1$

Put the given value of $m\angle 1=35\xb0$ in the above equation to write

$m\angle 2=35\xb0$

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

$m\angle 3+m\angle 4=180\xb0$

Put the given value of $m\angle 3=110\xb0$ in the above equation to write,

$\begin{array}{c}m\angle 4+110\xb0=180\xb0\\ m\angle 4=70\xb0\end{array}$

Finally, since in the figure c form a triangle, the sum of their measures should be equal to $180\xb0$. So,

$m\angle 2+m\angle 4+m\angle 5=180\xb0$

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

$\begin{array}{c}m\angle 5+70\xb0+35\xb0=180\xb0\\ m\angle 5=180\xb0-\left(35\xb0+70\xb0\right)\\ =180\xb0-105\xb0\\ =75\xb0\end{array}$

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