Answer:
The vertex angle of an isosceles triangle is the angle formed by the two congruent sides. In this case, the vertex angle has a measure of 52°.
To find the measure of one of the base angles, we can use the fact that the sum of the angles in a triangle is always 180°.
Since the isosceles triangle has two congruent sides, the base angles must also be congruent. Let's call the measure of each base angle x°.
We know that the sum of the vertex angle and the two base angles must equal 180°. So we can set up the equation:
52° + x° + x° = 180°
Combining like terms, we get:
52° + 2x° = 180°
Subtracting 52° from both sides, we have:
2x° = 128°
Dividing both sides by 2, we find:
x° = 64°
Therefore, the measure of one of the base angles is 64°.
So, the correct answer is (1) 64°.
Explanation: