2007 AMC 12A Problems/Problem 6

Problem

Triangles $ABC$ and $ADC$ are isosceles with $AB=BC$ and $\displaystyle AD=DC$ . 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:

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

2007 AMC 12A (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
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2007 AMC 12A Problems/Problem 6

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