One angle of a triangle is twice as large as the smallest angle. The measure of the third angle is 20 more than that of the smallest angle. Find the measure of the smallest angle.
2007-06-25 05:05:27 · 5 answers · asked by What's up people!! 1 in Science & Mathematics ➔ Mathematics
x = smallest angle
2x = another angle
x+20 = 3rd angle
4x+20 = 180
4x = 160
x= 40 = smallest angle
2x = 80 = 2nd angle
x+20 = 60 = 3rd angle
2007-06-25 05:12:44 · answer #1 · answered by ironduke8159 7 · 2⤊ 1⤋
You set up 3 equations for the 3 unknowns - the 3 angles of the triangle and then you solve the equations for the unknowns.
Call the 3 angles x, y and z.
You known:
x + y + z =180
Lets say z is the smallest angle.
Let x = 2z
y is the third angle. y = z + 20
Substitute x and y into the first equation.
2z + z + 20 = 180
Solve for z.
3z = 160
z = 160/3
You can know calculate x using the 2nd equation and y using the last equation.
2007-06-25 12:15:58 · answer #2 · answered by Scott H 3 · 0⤊ 0⤋
All angles must add up to 180:
a + b + c = 180
Let a be the smallest angle and b is twice as large:
a
2a = b
c, the third angle is 20 more than that of the smallest angle, a:
c = 20 + a
So:
a + 2a + 20 + a = 180
4a = 160
a = 40
b = 2a
b = 2(40)
b = 80
c = 20 + a
c = 20 + 40
c = 60
2007-06-25 12:14:00 · answer #3 · answered by yeeeehaw 5 · 0⤊ 2⤋
Relate everything to x. You know that the interior angles of a triangle = 180 degrees. So, setup your equation for the smallest angle, in terms of x:
180 = 2x + (x+20) + x.
Solve for x.
2007-06-25 12:14:17 · answer #4 · answered by miggitymaggz 5 · 0⤊ 0⤋
Smallest angle = x
Angle 2 = 2x
Angle 3 = x + 20
x + 2x + (x + 20) = 180
4x = 160
x = 40
Smallest angle is 40°
2007-06-29 04:57:46 · answer #5 · answered by Como 7 · 0⤊ 1⤋