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.
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Sum = x + x = 2x,
Vertex angle = (2X - 36).
2X + (2X - 36) = 180,
4X - 36 = 180,
4X = 180 + 36 = 216,
X = 216 / 4 = 54 DEG.
To find the number of degrees in the measure of one of the base angles of an isosceles triangle, we need to analyze the given information.
Let's assume that the measure of each base angle of the isosceles triangle is "x" degrees.
Since the triangle is isosceles, the two base angles are equal. Therefore, each base angle has a measure of "x" degrees.
The measure of the vertex angle is 36 degrees less than the sum of the measures of the base angles. The sum of the measures of the base angles is 2x.
So, the measure of the vertex angle is (2x - 36) degrees.
In a triangle, the sum of the three angles is always 180 degrees. Therefore, we can write the equation:
x + x + (2x - 36) = 180
Simplifying the equation:
4x - 36 = 180
Adding 36 to both sides:
4x = 216
Dividing both sides by 4:
x = 54
Therefore, each base angle of the isosceles triangle measures 54 degrees.