SOLUTION: Can you explain how to do these problems? thanks 19. the second angle of a triangle is two times as large as the first. The third angle is 10 more than the second angle. Find

Algebra ->  Formulas -> SOLUTION: Can you explain how to do these problems? thanks 19. the second angle of a triangle is two times as large as the first. The third angle is 10 more than the second angle. Find       Log On


   

Question 121685: Can you explain how to do these problems? thanks
19. the second angle of a triangle is two times as large as the first. The third angle is 10 more than the second angle. Find the measure of the first angle.
20. The perimeter of a rectangular writing pad is 28 inches. The length is 1 inch less than twice the width. Find the width.
thanks again
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
19. Let's call the angles A1, A2, A3.
1.A2=2%2AA1
2.A3=A2%2B10=2%2AA1%2B10
From your triangle knowledge you also know that the sum of the angles of a triangle equals 180 degrees.
3.A1%2BA2%2BA3=180
Now substitute your values from equation 1 and 2 into equation 3.
3.A1%2BA2%2BA3=180
A1%2B%282%2AA1%29%2B%282%2AA1%2B10%29=180
5%2AA1%2B10=180
5%2AA1=170
highlight%28A1=34%29
From 1,
1.A2=2%2AA1
A2=2%2A34
highlight%28A2=68%29
From 2,
2.A3=A2%2B10
A3=68%2B10
highlight%28A3=78%29
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20. The perimeter of a rectangular writing pad is 28 inches. The length is 1 inch less than twice the width. Find the width.
1.P=2W%2B2L=28
2.L=2W-1
Substitute 2 into 1 and solve for W.
1.2W%2B2L=28
2W%2B2%282W-1%29=28
2W%2B4W-2=28
6W-2=28
6W=30
highlight%28W=5%29
From 2,
2.L=2W-1
L=2%285%29-1
L=10-1
highlight%28L=9%29