one of the angle of triangl is 60 degree.the smaller angle of the other two angle is half of the greater.find all angles
180 - 60 = 120 degrees
x + 2x = 120
3x = 120
x = 40
The angles are
40, 80, and 60
g = the greater angle
s = the smaller angle = g / 2
The sum of the angles in a triangle is 180 °
60 ° + g + s = 180 °
60 ° + g / 2 + g = 180 °
60 ° + g / 2 + 2 g / 2 = 180 °
60 ° + 3 g / 2 = 180 ° Subtract 60 ° to both sides
3 g / 2 = 180 ° - 60 °
3 g / 2 = 120 ° Multiply both sides by 2
3 g = 2 * 120 °
3 g = 240 ° Divide both sides by 3
g = 240 ° / 3 = 80 °
s = g / 2 = 80 ° / 2 = 40 °
Angles:
the greater angle = 80 °
the smaller angle = 40 °
and given angle 60 °
To find all the angles of the triangle, we can use the given information to set up equations.
Let's denote the angles of the triangle as A, B, and C.
From the given information, one of the angles is 60 degrees. Therefore, let's assume angle A is 60 degrees.
According to the problem statement, the smaller angle of the other two angles is half of the greater angle. Let's denote the smaller angle as B and the greater angle as C.
So, we have:
A = 60 degrees
B = (1/2)C
The sum of the angles in a triangle is always 180 degrees. We can use this fact to set up an equation:
A + B + C = 180
Substituting the values from the given information, we get:
60 + (1/2)C + C = 180
Combining like terms, we have:
60 + (3/2)C = 180
Now, we can solve for C:
(3/2)C = 180 - 60
(3/2)C = 120
To isolate C, we divide both sides of the equation by (3/2):
C = (120 * 2) / 3
C = 240 / 3
C = 80
Now that we have C, we can find B using the relationship B = (1/2)C:
B = (1/2) * 80
B = 40
So, the angles of the triangle are:
A = 60 degrees
B = 40 degrees
C = 80 degrees