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(6938) About Me  (Show Source):
You can put this solution on YOUR website!

drawing%28350%2C350%2C-2%2C1%2C-1%2C2%2C+triangle%28-1.191753593%2C0%2C.1763269807%2C0%2C0%2C1%29%2C%0D%0Alocate%28-1.2%2C0%2CA%29%2C+locate%28.2%2C0%2CB%29%2C+locate%280%2C1.14%2CC%29++%0D%0A%0D%0A%29

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%27=%27%2C%27B-20%B0%27%29

Since matrix%281%2C7%2C+A%2C+%27%2B%27%2C+B%2C+%27%2B%27%2C+C%2C+%27=%27%2C+%27180%B0%27%29

1%2F2matrix%281%2C7%2C++++++B%2C++%27%2B%27%2C+B%2C+%27%2B%27%2C+%27%28B-20%B0%29%27%2C+%27=%27%2C+%27180%B0%27+++%29  

1%2F2matrix%281%2C9%2C++++++B%2C++%27%2B%27%2C+B%2C+%27%2B%27%2C+B%2C+%27-%27%2C+%2720%B0%27%2C+%27=%27%2C+%27180%B0%27+++%29

1%2F2matrix%281%2C7%2C++++++B%2C++%27%2B%27%2C+2B%2C+%27-%27%2C+%2720%B0%27%2C+%27=%27%2C+%27180%B0%27+++%29

Add %2720%B0%27 to both sides:

1%2F2matrix%281%2C5%2C++++++B%2C++%27%2B%27%2C+2B%2C++%27=%27%2C+%27200%B0%27+++%29

Multiply every term by 2 to clear of fractions:

matrix%281%2C2%2C%272%2A%27%2C1%2F2%29matrix%281%2C5%2C++++++B%2C++%27%2B%27%2C+2%2A2B%2C++%27=%27%2C+%272%2A200%B0%27+++%29

matrix%281%2C3%2Ccross%282%29%2C%27%2A%27%2C1%2Fcross%282%29%29matrix%281%2C5%2C++++++B%2C++%27%2B%27%2C+2%2A2B%2C++%27=%27%2C+%272%2A200%B0%27+++%29

matrix%281%2C5%2CB%2C+%27%2B%27%2C+4B%2C+%27=%27%2C+%27400%B0%27+%29+

matrix%281%2C3%2C+5B%2C+%27=%27%2C+%27400%B0%27%29

matrix%281%2C3%2C+B%2C+%27=%27%2C+%2780%B0%27%29

A+=+1%2F2matrix%281%2C6%2C+++++B%2C+%27=%27%2C+1%2F2%2C+%27%2A80%B0%27%2C+%27=%27%2C+%2740%B0%27%29+

matrix%281%2C7%2CC%2C%27=%27%2C%27B-20%B0%27%2C+%27=%27%2C+%2780%B0-20%B0%27%2C+%27=%27%2C%2760%B0%27++%29

drawing%28350%2C350%2C-2%2C1%2C-1%2C2%2C+triangle%28-1.191753593%2C0%2C.1763269807%2C0%2C0%2C1%29%2C%0D%0Alocate%28-1.2%2C0%2CA%29%2C+locate%28.2%2C0%2CB%29%2C+locate%280%2C1.14%2CC%29%2C+locate%28-.09%2C.15%2C%2780%B0%27%29%2C%0D%0Alocate%28-1%2C.15%2C%2740%B0%27%29%2C+locate%28-.16%2C.85%2C%2760%B0%27%29++%29

Edwin