vertex angle
angle between the two congruent sides
The vertex angle is the angle that is formed by the two congruent sides of an isosceles triangle at the vertex (point where the two sides meet). In the triangle, the non-vertex angle between the two congruent sides of the triangle is called the base angle. The vertex angle is always opposite to the base of the isosceles triangle.
Since the two sides of an isosceles triangle are congruent, the two base angles are also congruent. This means that if we know the measure of one base angle, we can find the measure of the other base angle by using the properties of angles in a triangle.
One important fact to remember is that the measure of the vertex angle of an isosceles triangle is always less than 180 degrees. This is because the sum of the angles in a triangle is always 180 degrees, and since one of the angles in an isosceles triangle is already fixed, the other two angles (the base angles) must add up to less than 180 degrees in order for the triangle to exist.
To find the measure of the vertex angle, we can use the formula:
vertex angle = 180 degrees – 2 x base angle
This formula works because the sum of the vertex angle and two base angles is always 180 degrees, and since the base angles are congruent, we can set them equal to x degrees and solve for the vertex angle.
For example, if one base angle of an isosceles triangle is 40 degrees, we can find the measure of the vertex angle as follows:
vertex angle = 180 degrees – 2 x 40 degrees
vertex angle = 100 degrees
Therefore, the measure of the vertex angle in this isosceles triangle is 100 degrees.
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