Question

The measure of the vertex angle of isosceles AABC is (x + 26). The measure of each base angle of AABC is (2x + 17). What is the measure of the vertex angle of AABC?

Answer 1

To find the measure of the vertex angle of an isosceles triangle, we can use the fact that an isosceles triangle has two equal base angles and the sum of all angles in a triangle is 180 degrees. By setting up an equation and solving for x, we can determine the measure of the vertex angle. In this case, the measure of the vertex angle is 50 degrees.

Step-by-step explanation:

The measure of the vertex angle of isosceles triangle ABC can be found by setting the measure of the vertex angle equal to (x + 26), where x represents an unknown value. Since an isosceles triangle has two equal base angles, each base angle can be represented by (2x + 17). In an isosceles triangle, the sum of the vertex angle and the base angles is always equal to 180 degrees. Therefore, we can set up the equation as follows:

(x + 26) + (2x + 17) + (2x + 17) = 180

Simplifying the equation: 5x + 60 = 180

Next, subtracting 60 from both sides and solving for x, we get:

5x = 120

x = 24

Substituting the value of x back into the equation for the vertex angle, we get:

(x + 26) = (24 + 26) = 50

Therefore, the measure of the vertex angle of isosceles triangle ABC is 50 degrees.