Final answer:
In an isosceles triangle ∆ABC with m∠A = 75°, the measure of ∠C is also 30° because the two base angles in an isosceles triangle are equal and the total sum of angles in a triangle is 180°.
Step-by-step explanation:
The question asks for the measure of ∆C in an isosceles triangle where m∠A = 75°. In an isosceles triangle, the two base angles are equal, and the sum of all angles in any triangle equals 180°. Since m∠A = 75° and it's given that ∆ABC is isosceles, we can assume that m∠B is also 75°. Therefore, to find m∠C, we subtract the sum of the two equal angles from 180°.
Step 1: Add the angles at A and B, which are both 75°.
180° - (75° + 75°) = 180° - 150°
Step 2: Subtract the sum of the two angles from 180° to find m∠C.
180° - 150° = 30°
Therefore, the measure of angle C in the given isosceles triangle ∆ABC is 30°.