Question 147506: The largest angle in a triangle is twice the degree measure of the second largest angle. One-third of the largest angle is 10 degrees larger than the difference of the other two. What is the measure in degrees of the smallest angle?
Answer by aswathytony(47)   (Show Source):
You can put this solution on YOUR website! Let the angle measures of the triangle be x, y ,z where x is largest angle measure, y is second largest angle measure & z is smallest angle measure.
given largest angle is twice second largest angle i.e. x = 2y ..........(1)
one third of largest angle is 10 more than difference of other two
i.e. 1/3 x = (y - z) +10...........(2)
substituting (1) in (2)
(1/3 )* 2y = (y - z) + 10 .
2y/3 = y - z +10
(2y/3) - y = - z + 10
(2y - 3y) /3 = -z + 10
-y = -3z +30
-y - 30 = -3z
y+30 = 3z
z = (y+30) /3 ........(3)
we know sum of angles of a triangle is 180deg
i.e. x + y+ z = 180
substituting (1) & (3) in above eq:
2y + y + (y + 30 )/3 = 180
6y + 3y + y + 30 = 180 * 3
10 y + 30 = 540
10y = 540 - 30 = 510
y = 510 / 10 = 51.
x = 2y = 2 * 51 = 102 degrees
z = (y+30)/3 =( 51 + 30 )/3 =81/3 = 27 degrees.
i.e measure of smallest angle is 27 degrees.
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