What is the measure of a base angle in an isosceles triangle if the vertex angle measures 40 degrees?

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In an isosceles triangle, two sides are of equal length, and the angles opposite those sides (the base angles) are also equal. The vertex angle is the angle formed by the two equal sides.

To find the measure of the base angles when the vertex angle is given, we can use the properties of triangles. The sum of all angles in any triangle is always 180 degrees.

In this case, since the vertex angle measures 40 degrees, we can set up the following equation for the base angles (let’s denote the measure of each base angle as θ):

   Vertex Angle + Base Angle 1 + Base Angle 2 = 180 degrees

This boils down to:

   40 degrees + θ + θ = 180 degrees

Simplifying the equation, we get:

   40 degrees + 2θ = 180 degrees

Next, we subtract 40 degrees from both sides:

   2θ = 180 degrees - 40 degrees
   2θ = 140 degrees

Now, divide both sides by 2 to solve for θ:

   θ = 140 degrees / 2
   θ = 70 degrees

Therefore, the measure of each base angle in the isosceles triangle is 70 degrees.

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