Final answer:
The two base angles of an isosceles triangle are equal and given as 35° each. To find the vertex angle, subtract the base angles (sum of 70°) from the total sum of 180°, which gives 110° for the vertex angle.
Step-by-step explanation:
If an isosceles triangle has a base angle that measures 35°, we can find the measures of the other angles by understanding a few basic properties of triangles. The two base angles of an isosceles triangle are equal and given as 35° each. To find the vertex angle, subtract the base angles (sum of 70°) from the total sum of 180°, which gives 110° for the vertex angle.
First, by definition, an isosceles triangle has two sides of equal length, and the angles opposite those sides are also equal. Second, the sum of the interior angles in any triangle is 180°.
Since the triangle is isosceles and one base angle is given as 35°, the other base angle must also be 35°. Now, to find the measure of the triangle's vertex angle, we subtract the sum of the base angles from 180°: 180° - 35° - 35° = 110°.
Therefore, the measures of the two base angles are 35° each, and the measure of the vertex angle is 110°.