In an isosceles triangle, there are two equal angles, called the base angles, and one vertex angle. We know that the sum of all angles in any triangle is always 180 degrees.
Given that the vertex angle measures 40 degrees, we can find the measure of each base angle as follows:
Let the measure of each base angle be denoted as θ. Since there are two base angles, we can set up the equation:
40 + θ + θ = 180
Simplifying this gives:
40 + 2θ = 180
Subtracting 40 from both sides gives:
2θ = 180 – 40
2θ = 140
Now, dividing both sides by 2 gives:
θ = 70
Hence, the measure of each base angle in the isosceles triangle is 70 degrees.