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Difference between revisions of "2007 AMC 12A Problems/Problem 6"

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{{duplicate|[[2007 AMC 12A Problems|2007 AMC 12A #6]] and [[2007 AMC 10A Problems/Problem 8|2007 AMC 10A #8]]}}
 
==Problem==
 
==Problem==
 
Triangles <math>ABC</math> and <math>ADC</math> are [[isosceles]] with <math>AB=BC</math> and <math>AD=DC</math>. Point <math>D</math> is inside triangle <math>ABC</math>, angle <math>ABC</math> measures 40 degrees, and angle <math>ADC</math> measures 140 degrees. What is the degree measure of angle <math>BAD</math>?
 
Triangles <math>ABC</math> and <math>ADC</math> are [[isosceles]] with <math>AB=BC</math> and <math>AD=DC</math>. Point <math>D</math> is inside triangle <math>ABC</math>, angle <math>ABC</math> measures 40 degrees, and angle <math>ADC</math> measures 140 degrees. What is the degree measure of angle <math>BAD</math>?
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==See also==
 
==See also==
 
{{AMC12 box|year=2007|ab=A|num-b=5|num-a=7}}
 
{{AMC12 box|year=2007|ab=A|num-b=5|num-a=7}}
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{{AMC10 box|year=2007|ab=A|num-b=7|num-a=9}}
  
 
[[Category:Introductory Geometry Problems]]
 
[[Category:Introductory Geometry Problems]]

Revision as of 18:04, 5 January 2008

The following problem is from both the 2007 AMC 12A #6 and 2007 AMC 10A #8, so both problems redirect to this page.

Problem

Triangles $ABC$ and $ADC$ are isosceles with $AB=BC$ and $AD=DC$. Point $D$ is inside triangle $ABC$, angle $ABC$ measures 40 degrees, and angle $ADC$ measures 140 degrees. What is the degree measure of angle $BAD$?

$\mathrm{(A)}\ 20\qquad \mathrm{(B)}\ 30\qquad \mathrm{(C)}\ 40\qquad \mathrm{(D)}\ 50\qquad \mathrm{(E)}\ 60$

Solution

2007 AMC12A-6.png

We angle chase, and find out that:

  • $DAC=\frac{180-140}{2} = 20$
  • $BAC=\frac{180-40}{2} = 70$
  • $BAD=BAC-DAC=50\ \mathrm{(A)}$

See also

2007 AMC 12A (Problems • Answer Key • Resources)
Preceded by
Problem 5 		Followed by
Problem 7
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 AMC 12 Problems and Solutions
2007 AMC 10A (Problems • Answer Key • Resources)
Preceded by
Problem 7 		Followed by
Problem 9
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 AMC 10 Problems and Solutions
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