Difference between revisions of "2014 AMC 8 Problems/Problem 9"
(→Solution) |
(→Solution) |
||
| (6 intermediate revisions by 5 users not shown) | |||
| Line 15: | Line 15: | ||
<math>\textbf{(A) }100\qquad\textbf{(B) }120\qquad\textbf{(C) }135\qquad\textbf{(D) }140\qquad \textbf{(E) }150</math> | <math>\textbf{(A) }100\qquad\textbf{(B) }120\qquad\textbf{(C) }135\qquad\textbf{(D) }140\qquad \textbf{(E) }150</math> | ||
| + | |||
| + | ==Video Solution (CREATIVE THINKING)== | ||
| + | https://youtu.be/jLnqUOe0HPE | ||
| + | |||
| + | ~Education, the Study of Everything | ||
| + | |||
| + | |||
==Video Solution== | ==Video Solution== | ||
| − | https://www.youtube.com/watch?v=HP-lBKohxhE | + | https://www.youtube.com/watch?v=HP-lBKohxhE ~David |
| + | |||
| + | https://youtu.be/j5KrHM81HZ8 ~savannahsolver | ||
| + | |||
| + | ==Video Solution == | ||
| + | https://youtu.be/abSgjn4Qs34?t=3140 | ||
==Solution== | ==Solution== | ||
| − | <math>BD = DC</math>, so <math>\angle DBC = \angle DCB = 70</math>. Then <math>\angle CDB = 180-(70+70) = 40</math>. Since <math>\angle ADB</math> and <math>\angle BDC</math> are supplementary, <math>\angle ADB = 180 - 40 = \boxed{\textbf{(D)}~140}</math>. | + | Using angle chasing is a good way to solve this problem. <math>BD = DC</math>, so <math>\angle DBC = \angle DCB = 70</math>, because it is an isosceles triangle. Then <math>\angle CDB = 180-(70+70) = 40</math>. Since <math>\angle ADB</math> and <math>\angle BDC</math> are supplementary, <math>\angle ADB = 180 - 40 = \boxed{\textbf{(D)}~140}</math>. |
==See Also== | ==See Also== | ||
{{AMC8 box|year=2014|num-b=8|num-a=10}} | {{AMC8 box|year=2014|num-b=8|num-a=10}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Latest revision as of 20:32, 16 June 2024
Contents
Problem
In 
, 
is a point on side 
such that 
and 
measures 
. What is the degree measure of 
?
![[asy] size(300); defaultpen(linewidth(0.8)); pair A=(-1,0),C=(1,0),B=dir(40),D=origin; draw(A--B--C--A); draw(D--B); dot("$A$", A, SW); dot("$B$", B, NE); dot("$C$", C, SE); dot("$D$", D, S); label("$70^\circ$",C,2*dir(180-35));[/asy]](http://latex.artofproblemsolving.com/9/4/7/94770df9a0e1d5a71f602bfb3b45022dcca9dec4.png)
Video Solution (CREATIVE THINKING)
~Education, the Study of Everything
Video Solution
https://www.youtube.com/watch?v=HP-lBKohxhE ~David
https://youtu.be/j5KrHM81HZ8 ~savannahsolver
Video Solution
https://youtu.be/abSgjn4Qs34?t=3140
Solution
Using angle chasing is a good way to solve this problem. 
, so 
, because it is an isosceles triangle. Then 
. Since and 
are supplementary, 
.
See Also
| 2014 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
