what is the difference between the measures of the largest and smallest angles of the triangle? (I keep getting 40 and that is incorrect) Please explain how you got the answer THANKS!
2007-12-26 09:14:35 · 12 answers · asked by staciaschool2 2 in Science & Mathematics ➔ Mathematics
8x + 20 = 180
8x = 160
x = 20
Angles are 60° , 30° , 90°
Difference = 60°
2007-12-30 05:17:46 · answer #1 · answered by Como 7 · 0⤊ 0⤋
Sum of measures of all angles of a triangle = 180
3x + 2x - 10 + 3x + 30 = 180
3x + 2x + 3x -10 + 30 = 180
8x + 20 = 180
8x = 180 - 20
8x = 160
x = 160 / 8
x = 20
The angles are
3x = 3(20) = 60
2x - 10 = 2(20) - 10 = 40 - 10 = 30
3x + 30 = 3(20) +30 = 60 + 30 = 90
Difference between largest and smallest angles = 90 - 30 = 60
Hope that helps
2007-12-26 09:19:34 · answer #2 · answered by gmat g 3 · 0⤊ 0⤋
the sum of the angles of a triangle is 180.
So you add them all and find the x value
3x+2x-10+3x+30=180
8x+20=180
8x=160
x=20
therefore the 1st angle is 3*20=60
2nd angle is 2*20-10=30
3rd angle is 3*20+30=90
so the difference b/n the largest and the smallest angle is 90-30=60
so the answer is 60
2007-12-28 00:03:49 · answer #3 · answered by xmashi 3 · 0⤊ 0⤋
3x + (2x - 10) + (3x + 30) = 180
8x + 20 = 180
8x = 160
x = 20
Largest angle = 3x + 30 = 90
Smallest angle = 2x - 10 = 30
Difference = 60
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Explanation
The sum of the measures of the angles of a triangle is 180. So I added all the angles and solved for x. After solving for x, I determine which is the largest and which is the smallest. Then you find the difference and you're done.
2007-12-26 09:18:45 · answer #4 · answered by UnknownD 6 · 0⤊ 0⤋
the interior angle measures of a triangle are 180 degrees so:
3x+2x-10+3x+30=180
8x+20=180
subtract 20 from both sides
8x=160
divide bot sides by 8
x=20.
angle 1=3x degrees
measure of angle 1= 3(20)
so 3x=60
angle 2 is 2x-10 degrees
2(20)-10
40-10
angle 2 or 2x-10=30 degrees
you can solve for the last angle 2 ways.
one is the same way you did the other two, by substituting x for 20:
angle 3=3x+30
3(20)+30
60+30
90 degrees.
or, because you know the sum of the interior angle measures is always 180, you can say:
180=angle 1+angle2+ angle 3
180=60+30+m (m=measure of angle 3)
180=90+m
subtract 90 from both sides and you get:
measure of angle 3=90 degrees
Now that you know that the largest angle is 90 degreesand the smallest one is 30 you subtract 30 from 90 to find your answer which is 60
2007-12-26 09:27:13 · answer #5 · answered by hillhavengirl 2 · 0⤊ 0⤋
The sum of all angles of a triangle must equal 80. so the sum of all the equations must equal 80.
(3x)+(2x-10)+(3x+30) = 180
solve for x
3x+2x+3x+30-10 = 180
8x + 20 = 180
8x = 160
x = 20
plug x in to the angles
3x = 3(20) = 60
2x-10 = 2(20)-10 = 30
3x+30=3(20)+30 = 90
60+30+90 = 180 so this shoudl be correct.
the difference then is 60-30 = 30
2007-12-26 09:20:07 · answer #6 · answered by daman b 1 · 0⤊ 0⤋
3x + (2x - 10) + (3x + 30) = 180 degrees
simplify:
8x + 20 = 180
x = 160 / 8 = 20
3x = 60 degrees
2x - 10 = 30 degrees
3x + 30 = 90 degrees
the angle between the largest and smallest:
90 degrees - 30 degrees
= 60 degrees
2007-12-26 09:23:09 · answer #7 · answered by Anonymous · 0⤊ 0⤋
3x + 2x - 10 + 3x + 30 = 180
8x + 20 = 180
8x = 160
x = 20
So the angle are
30 ,60, 90
90 - 30 = 60
Good luck!
2007-12-26 09:23:10 · answer #8 · answered by Ken 7 · 0⤊ 0⤋
Ok,
Well you know that 3x + (2x - 10) + (3x + 30) =180
So by combination we can say 8x + 20 = 180
Therefore 8x = 160
So x =20
3x = 60
2x - 10 = 30 (Smallest)
3x + 30 = 90
60 + 30 + 90 = 180
I hope this helps
2007-12-26 09:19:31 · answer #9 · answered by Charles Q 2 · 0⤊ 0⤋
3x + (2x - 10) + (3x + 30) = 180
8x + 20 = 180
8x = 160
x = 20
ok thanks
2007-12-26 21:27:08 · answer #10 · answered by sanjeewa 4 · 0⤊ 0⤋