SOLUTION: in a certain triangle the measure of the measure of the second angle is 10 degrees greater than three times the first. the third angle measure is equal to the sum of the measures o

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Question 523971: in a certain triangle the measure of the measure of the second angle is 10 degrees greater than three times the first. the third angle measure is equal to the sum of the measures of the other two. Find the measures of the three angles.
Found 3 solutions by lwsshak3, solver91311, lagbens:
Answer by lwsshak3(11628) About Me  (Show Source):
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in a certain triangle the measure of the measure of the second angle is 10 degrees greater than three times the first. the third angle measure is equal to the sum of the measures of the other two. Find the measures of the three angles.
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let x=measure of first angle
3x+10=measure of second angle
x+(3x+10)=measure of third angle
..
x+(3x+10)+(x+(3x+10))=180
x+3x+10+x+3x+10=180
8x=180-20=160
x=20º
ans:
measure of first angle=20º
measure of second angle=70º
measure of third angle=90º

Answer by solver91311(24713) About Me  (Show Source):
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The only way that the measure of a 3rd angle of a triangle can be equal to the sum of the measure of the other two angles is if the 3rd angle is a right angle. That means the sum of the other two angles must be .

Proof:

Let represent the first angle and let represent the second angle. Then the third angle has to be

The sum of the angles in any triangle is , so:







Hence:

Since we have let represent the second angle, we can say the first angle must be , and then, by substitution:



Solve for then calculate

John

My calculator said it, I believe it, that settles it
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Answer by lagbens(14) About Me  (Show Source):
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let's call the 1st angle X, so the 2nd angle would be equal to 10+3X.
the 3rd angle is equal to 10+3X+X which is 10+4x.
the total measure of the 3 angles of a triangle is 180 degree.
so we can write X+10+3X+10+4X=180.
okay we have an equation now, let's solve for "X"
8X+20=180(subtract both side by 20)
8X=160(divide both side by 8)
X=20 (1st angle)
10+3(20)=70 (2nd angle)
10+4(20)=90 (3rd angle)