the measures of the interior angles of a triangle are x,y and 2x respectively. if the triangle is isosceles, what is one possible measure of an angle of this triangle, in degrees?
if x and y are the equal angles,
then
x+y+2x = 180
x+x+2x=180
x = 45
angles: 45, 45, 90
if the x and 2x are the equal angles
then
x + y + 2x = 180
x+2x+2x=180
x = 36
angles:
36, 72, 72
To solve this problem, we can use the fact that the sum of the interior angles of a triangle is always 180 degrees.
Let's assume that the measures of the interior angles are x, y, and 2x. Since the triangle is isosceles, we know that two of the angles are equal.
Let's use the equation for the sum of the angles:
x + y + 2x = 180
Combine the like terms:
3x + y = 180
Since we know that two of the angles are equal, we can set up an equation:
x = y
Substitute x with y in the equation we obtained earlier:
3y + y = 180
Combine the like terms again:
4y = 180
Divide both sides by 4:
y = 45
Therefore, one possible measure of an angle in this triangle is 45 degrees.