Find the number of degrees in the measure of one of the base angles of an isosceles triangle, if the measure of the vertex angle is 36 degrees less than the sum of the measures of the base angles.
let each base angle be x
then the vertex angle is 2x-36
solve
x + x + 2x-36 = 180
To find the number of degrees in the measure of one of the base angles of an isosceles triangle, let's first assign a variable to represent the measure of one of the base angles. Let's call it "x".
Since an isosceles triangle has two congruent (equal) base angles, the measure of the other base angle will also be "x".
The vertex angle is the angle formed by the two congruent sides of the isosceles triangle. According to the problem, the measure of the vertex angle is 36 degrees less than the sum of the measures of the base angles (2x).
So, the measure of the vertex angle is (2x - 36) degrees.
Now, we know that the sum of the interior angles of a triangle is always 180 degrees. We can use this information to create an equation and solve for "x".
The equation becomes:
x + x + (2x - 36) = 180
Combining like terms, we simplify the equation:
4x - 36 = 180
Next, let's isolate the variable by adding 36 to both sides of the equation:
4x = 216
Finally, divide both sides of the equation by 4 to solve for "x":
x = 54
Therefore, one of the base angles of the isosceles triangle measures 54 degrees.