In an isoceles triangle top vertex is twice the of the sum of the base angle.find all the exterior angles of the triangle?
If it is an isosceles triangle the two base angles will be equal.
Let the base angle be a, then the vertex angle will be:
180° - 2 a
According to the condition:
Top vertex is twice the of the sum of the base angle:
180° - 2 a = 2 ( a + a )
180° - 2 a = 2 * 2a
180° - 2 a = 4 a Add 2 a to both sides
180° - 2 a + 2 a = 4 a + 2 a
180° = 6 a Divide both sides by 6
180° / 6 = a
30° = a
a = 30 °
So the base angles are 30° and the vertex angle is 180° - 2 * 30° = 180° - 60° = 120 °
Exterior base angle is 360° - 30° = 330°
The exterior vertex angle is 360° - 120° = 240°
I believe exterior angles are 180 - interior angles. Their sum is 360.
To find the exterior angles of an isosceles triangle, we need to know that the sum of the exterior angles of any polygon is always 360 degrees.
First, let's find the measure of the top vertex angle of the isosceles triangle. Let's call this angle "A".
According to the given information, the top vertex angle "A" is twice the sum of the base angles, let's call these angles "B".
So we have the equation: A = 2B
In an isosceles triangle, the base angles are congruent, meaning they have equal measures. Let's call the measure of each base angle "x".
So, we can write the equation for the sum of the base angles as: 2x
Since the top vertex angle "A" is twice the sum of the base angles, we can substitute the value of "2x" into the equation for "A" as follows: A = 2(2x)
Simplifying this equation, we get: A = 4x
Now, we have the measure of the top vertex angle "A" in terms of "x".
To find the value of "x", we can use the fact that the angles in a triangle add up to 180 degrees.
In an isosceles triangle, we have: A + 2B = 180
Substituting the values of "A" and "B", we get: 4x + 2x + 2x = 180
Simplifying this equation, we get: 8x = 180
Dividing both sides of the equation by 8, we find: x = 22.5
Now, we know the measure of each base angle is 22.5 degrees.
Finally, to find the measure of the exterior angles, we subtract the base angle from 180 degrees (since the exterior angle and the base angle form a linear pair).
So, each exterior angle of the isosceles triangle measures: 180 - 22.5 = 157.5 degrees.
Therefore, all the exterior angles of the isosceles triangle measure 157.5 degrees each.