15.10: Chapter 10
- Page ID
- 129939
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Your Turn
/**/\overleftrightarrow {RS} \bot \overleftrightarrow {XY}/**/
/**/\overleftrightarrow {UV} \bot \overleftrightarrow {XY}/**/
Acute Angles | Obtuse Angles | Right Angles | Straight Angles |
---|---|---|---|
/**/\angle AOB/**/ /**/\angle AOC/**/ /**/\angle BOC/**/ /**/\angle BOD/**/ /**/\angle COD/**/ /**/\angle DOE/**/ /**/\angle FOE/**/ |
/**/\angle AOE/**/ /**/\angle BOF/**/ /**/\angle COF /**/ |
/**/\angle AOD/**/ /**/\angle BOE/**/ /**/\angle DOF /**/ |
/**/\angle AOF/**/ |
Callstack:
at (Bookshelves/Applied_Mathematics/Contemporary_Mathematics_(OpenStax)/15:_Answer_Key/15.10:_Chapter_10), /content/body/div/div/div/div[8]/div/span/span[1], line 1, column 4
Callstack:
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/**/m\measuredangle 6 = {62^ \circ }/**/
/**/m\measuredangle 7 = {118^ \circ }/**/
/**/m\measuredangle 8 = {62^ \circ }/**/
/**/m\measuredangle 9 = {118^ \circ }/**/
The sum of the interior angles is /**/{540^ \circ }/**/.
![Three hexagons are graphed on a grid. Hexagon, A B C D E F is plotted. The bottom and top sides, A F and C D measure 3 units, each. The other sides, C B, B A, D E, and E F measure 2 units, each. The hexagon is translated 5 units to the right and 3 units up. The vertices of the translated hexagon are A prime, B prime, C prime, D prime, E prime, and F prime. The translated hexagon is again translated 7 units down. The vertices of the newly translated hexagon are A double prime, B double prime, C double prime, D double prime, E double prime, and F double prime.](https://math.libretexts.org/@api/deki/files/110085/CS_Figure_10_05_UN004.png?revision=1)
![CS_Figure_10_05_UN016.png](https://math.libretexts.org/@api/deki/files/110086/CS_Figure_10_05_UN016.png?revision=1)
Check Your Understanding
/**/\begin{array}{*{20}{rcl}}{\frac{3}{2}}&{ = }&{\frac7{x}} \\ {3x}&{ = }&{14} \\ {x}&{ = }&{\frac14{3}} \\ \end{array}/**/ | /**/\begin{array}{*{20}{rcl}}{\frac{4}{2}}&{ = }&{\frac (click for details) Callstack:
at (Bookshelves/Applied_Mathematics/Contemporary_Mathematics_(OpenStax)/15:_Answer_Key/15.10:_Chapter_10), /content/body/div/div/div/div[76]/div/div[20]/div/table/tbody/tr/td[2]/span/span[1], line 1, column 5
(click for details) } \\{\frac14{3}(4)}&{ = }&{2(4 + y)} \\{\frac56{3}}&{ = }&{8 + 2y} \\{56}&{ = }&{3(8 + 2y)} \\{56}&{ = }&{24 + 6y} \\{32}&{ = }&{6y} \\{\frac16{3}}&{ = }&{y}\end{array}/**/ Callstack:
at (Bookshelves/Applied_Mathematics/Contemporary_Mathematics_(OpenStax)/15:_Answer_Key/15.10:_Chapter_10), /content/body/div/div/div/div[76]/div/div[20]/div/table/tbody/tr/td[2]/span/span[2], line 1, column 1
|
/**/\begin{array}{*{20}{rcl}}{\frac{6}{a}}&{ = }&{\frac1214} \\{6(14)}&{ = }&{12a} \\{84}&{ = }&{12a} \\{7}&{ = }&{a}\end{array}/**/
Thus, /**/t = 20/**/ and /**/a = 7./**/