In an isosceles triangle, the measure of the vertex angle is 4x. The measure of each base angle is 2x + 10. What is the actual measure of the vertex angle?
4X + 2(2X + 10) = 180
8X = 160
X = 20 Deg.
To find the measure of the vertex angle, we need to solve for x.
In an isosceles triangle, the vertex angle and base angles are equal. So, we can set up an equation:
4x = 2x + 10
Now, let's solve for x.
4x - 2x = 10
2x = 10
Dividing both sides by 2:
x = 5
Now that we have found the value of x, we can substitute it back into the equation for the vertex angle to find its measure.
Vertex angle = 4x = 4(5) = 20
Therefore, the actual measure of the vertex angle is 20.
To find the actual measure of the vertex angle in an isosceles triangle, you need to determine the value of x and then substitute it into the given equation.
Given:
Measure of each base angle = 2x + 10
Measure of the vertex angle = 4x
Since the triangle is isosceles, the base angles are equal. So, the equation can be written as:
2x + 10 = 2x + 10
Now, solve the equation:
2x + 10 - 2x = 4x - 2x + 10 - 10
10 = 2x
Now, divide both sides of the equation by 2:
10/2 = 2x/2
5 = x
Now that we have the value of x, substitute it into the equation for the measure of the vertex angle:
Measure of the vertex angle = 4x
= 4(5)
= 20
So, the actual measure of the vertex angle is 20.