The sum of two angels of a triangle is 116 degree and their difference is 24 degree . find the measure of each angle of the triangle.
y+x = 116
y-x = 24
Now just solve for x,y and 180-(x+y)
To find the measure of each angle of the triangle, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
Let's assume the measure of one of the angles in the triangle is x degrees. Then, the measure of the second angle can be expressed as (x + 24) degrees because their difference is 24 degrees.
According to the problem statement, the sum of the two angles is 116 degrees. Therefore, we can write the equation:
x + (x + 24) = 116
Simplifying the equation, we combine like terms:
2x + 24 = 116
Now, let's isolate the term with x:
2x = 116 - 24
2x = 92
To solve for x, divide both sides of the equation by 2:
x = 92 / 2
x = 46
So, one of the angles in the triangle is 46 degrees. To find the measure of the second angle, we substitute it into (x + 24):
46 + 24 = 70
Therefore, the measure of each angle of the triangle is 46 degrees, 70 degrees, and the third angle can be calculated by subtracting the sum of the first two angles from 180 degrees:
180 - (46 + 70) = 180 - 116 = 64 degrees.
In conclusion, the angles of the triangle measure 46 degrees, 70 degrees, and 64 degrees.