2007 AMC 12A Problems/Problem 6

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(Redirected from 2007 AMC 10A Problems/Problem 8)

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

We angle chase, and find out that:

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

2007 AMC 12A (Problems)
Preceded by Problem 5	Followed by Problem 7
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2007 AMC 10A (Problems)
Preceded by Problem 7	Followed by Problem 9
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2007 AMC 12A Problems/Problem 6

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