Final answer:
In an isosceles trapezoid ABCD, ∠B = ∠C = 80° and ∠A = ∠D = 100°.
Step-by-step explanation:
In an isosceles trapezoid ABCD, AB || DC, AD = BC, and ∠C = 80°.
To find the measures of the remaining angles, we can use the fact that the sum of the angles in a quadrilateral is 360°.
In this case, since AB || DC, angles B and C are congruent.
Therefore, ∠B = ∠C = 80°.
Since AD = BC, angles A and D are congruent. Therefore, ∠A = ∠D.
The sum of the angles ∠A, ∠B, ∠C, and ∠D in the isosceles trapezoid ABCD is equal to 360°.
Therefore, ∠A + ∠B + ∠C + ∠D = 360°. Substituting the known values, we have ∠A + 80° + 80° + ∠A = 360°.
Simplifying the equation, we have 2∠A + 160° = 360°. Subtracting 160° from both sides, we get 2∠A = 200°.
Dividing both sides by 2, we find that ∠A = ∠D = 100°.