An isosceles triangle has one angle of 64°. Its other two angles are the same size as each other. What does each angle measure?
Since it is an isosceles triangle, two angles are equal in measure. Let's denote these angles as x.
According to the triangle angle sum theorem, the sum of all angles in a triangle is 180 degrees.
Therefore, we can write the equation:
64 + x + x = 180
Combining like terms, we have:
64 + 2x = 180
Subtracting 64 from both sides, we get:
2x = 116
Dividing both sides by 2, we find:
x = 58
So, each of the equal angles in the isosceles triangle measures 58 degrees.
In an isosceles triangle, the two equal angles are opposite to the two equal sides. Since one angle is given as 64°, the other two angles must be the same. To find the measure of each angle, we can subtract the given angle from 180° (the sum of all angles in a triangle) and then divide by 2.
180° - 64° = 116°
116° ÷ 2 = 58°
Therefore, each angle of the isosceles triangle measures 58°.