SOLUTION: In a triangle the measure of the first angle is one-half the measure of the second angle. The third angle's measure is 20° less than the measure of the second angle. What are the m

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Question 172325This question is from textbook
: In a triangle the measure of the first angle is one-half the measure of the second angle. The third angle's measure is 20° less than the measure of the second angle. What are the measures of the angles? This question is from textbook

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!



Let 

A = first angle,
B = second angle
C = third angle

the measure of the first angle is one-half the measure of the second angle.

So A+=+1%2F2B

The third angle's measure is 20° less than the measure of the second angle

So matrix%281%2C3%2CC%2C%22=%22%2C%22B-20%B0%22%29

Since matrix%281%2C7%2C+A%2C+%22%2B%22%2C+B%2C+%22%2B%22%2C+C%2C+%22=%22%2C+%22180%B0%22%29

1%2F2  

1%2F2

1%2F2

Add %2220%B0%22 to both sides:

1%2F2matrix%281%2C5%2C++++++B%2C++%22%2B%22%2C+2B%2C++%22=%22%2C+%22200%B0%22+++%29

Multiply every term by 2 to clear of fractions:

matrix%281%2C2%2C%222%2A%22%2C1%2F2%29matrix%281%2C5%2C++++++B%2C++%22%2B%22%2C+2%2A2B%2C++%22=%22%2C+%222%2A200%B0%22+++%29

matrix%281%2C3%2Ccross%282%29%2C%22%2A%22%2C1%2Fcross%282%29%29matrix%281%2C5%2C++++++B%2C++%22%2B%22%2C+2%2A2B%2C++%22=%22%2C+%222%2A200%B0%22+++%29

matrix%281%2C5%2CB%2C+%22%2B%22%2C+4B%2C+%22=%22%2C+%22400%B0%22+%29+

matrix%281%2C3%2C+5B%2C+%22=%22%2C+%22400%B0%22%29

matrix%281%2C3%2C+B%2C+%22=%22%2C+%2280%B0%22%29

A+=+1%2F2matrix%281%2C6%2C+++++B%2C+%22=%22%2C+1%2F2%2C+%22%2A80%B0%22%2C+%22=%22%2C+%2240%B0%22%29+





Edwin