In an isosceles triangle angle in the top vertex is twice the sum of the base angle. Find the exterior angles of the triangle.
Let vertex is x
Basa angles are 2x
We know that
Sum of angles in triangle is 180
X+2x+2x=180
5x= 180
X=36
Base angle=2(36)
=72
Exterior angles = sum of interior angles
=72+72
=144
To find the exterior angles of an isosceles triangle, you need to know that the sum of all exterior angles of any polygon is always 360 degrees.
In an isosceles triangle, two of the angles are congruent (the base angles), and one angle is different (the top angle or vertex angle). Let's call the top angle "x" and the base angle "y".
According to the given information, the top angle is twice the sum of the base angles. That can be expressed as:
x = 2y
Since all three angles of a triangle add up to 180 degrees, we can also express the sum of the base angles as:
2y + 2y + x = 180
Substituting the value of x from the first equation into the second equation, we get:
2y + 2y + 2y = 180
6y = 180
Dividing both sides of the equation by 6, we find:
y = 30
Now we can substitute the value of y into the first equation to find the value of x:
x = 2y
x = 2 * 30
x = 60
So, the top angle (x) is 60 degrees, and each base angle (y) is 30 degrees.
The exterior angles of a triangle are formed by extending one side of the triangle. In an isosceles triangle, each exterior angle is equal in measure to the sum of the two remote interior angles. Therefore, the measure of each exterior angle is:
Exterior angle = Base angle + Base angle
Exterior angle = 30 + 30
Exterior angle = 60 degrees
Hence, each exterior angle of this isosceles triangle measures 60 degrees.