Question 79832This question is from textbook
: The second angle of a triangle is three times the first, and the third is 5 degrees more than the first. Find the measures of the angles.
I have no idea where to start.Thanks soo much!
This question is from textbook
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Well, one very good place to start is by remembering that the sum of the angles in any plane (flat) triangle is always 180 degrees.
Let's number the angles of your triangle:
< 1 This is the first angle
< 2 The second angle.
< 3 The third angle.
From the problem description, you can write:
<2 = 3*(<1) "The second angle is three times the first".
<3 = <1+5 "The third is 5 degrees more than the first".
Now we can put all of this together to make an equation.
<1+<2+<3 = 180 "The sum of the angles ...is 180 degrees"
Now we make some substitutions for angle <2 and for angle <3
<1+(3*<1)+(<1+5) = 180 Ok so far? Now simplify this to find the measure of angle 1.
5*<1 + 5 = 180 Subtract 5 from both sides.
5*<1 = 175 Finally, divide both sides by 5.
<1 = 35 degrees. Now we've found angle 1, we can find angles 2 and 3.
<2 = 3*<1
<2 = 3*35
<2 = 105 degrees.
<3 = <1+5
<3 = 35+5
<3 = 40 degrees.
Check:
<1+<2+<3 = 35+105+40 = 180
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