SOLUTION: The ratio of the measures of an interior angle of the triangle to the measure of its adjacent exterior angle is 4 to 5. thank you!

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Question 935953: The ratio of the measures of an interior angle of the triangle to the measure of its adjacent exterior angle is 4 to 5.
thank you!
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
The exterior angle is supplemental to the adjoining interior angle.
if an interior angle alpha and exterior angle gamma, then

alpha%2Bgamma=180.........eq.1
alpha%2Fgamma=4%2F5.........eq.2
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alpha%2Fgamma=4%2F5.........eq.2 ...solve for alpha
alpha=%284%2F5%29gamma....substitute in eq.1
%284%2F5%29gamma%2Bgamma=180.........eq.1 ...solve for gamma
%284%2F5%29gamma%2B%285%2F5%29gamma=180
%289%2F5%29gamma=180
gamma=180%2F%289%2F5%29
gamma=%28180%2A5%29%2F9
highlight%28gamma=100%29...- exterior angle
then alpha=180-100=>highlight%28alpha=80%29...- interior angle

check ratio:
80%3A100=4%3A5
80%2F100=4%2F5
4%2F5=4%2F5