Find the vertex angle of an isosceles triangle if it exceeds each base angle by 30 degree.
since the two base angles are equal, if each is x, then
x+30 + x + x = 180
3x = 150
x = 50
So, the vertex angle is 80
To find the vertex angle of an isosceles triangle, we need to know the measure of either the base angle or the length of the base. In this case, let's assume we know the measure of the base angle.
Let's call the measure of each base angle x degrees. According to the given information, the vertex angle exceeds each base angle by 30 degrees. Therefore, the measure of the vertex angle would be x + 30 degrees.
Since an isosceles triangle has two congruent base angles, we can write the equation:
2x + x + 30 = 180
To solve for x, we combine like terms:
3x + 30 = 180
Subtract 30 from both sides of the equation:
3x = 150
Divide both sides of the equation by 3:
x = 50
Now that we have the measure of each base angle, we can find the measure of the vertex angle:
Vertex angle = x + 30 = 50 + 30 = 80 degrees
Therefore, the vertex angle of the isosceles triangle is 80 degrees.