To determine the measure of $\angle ADC$ in quadrilateral $ABCD$, let's analyze the properties of the shape and the information given:

1. Identify the Shape: Quadrilateral $ABCD$ appears to be an isosceles trapezoid because it has one pair of parallel sides ($AB$ and $CD$), and the non-parallel sides ($AD$ and $BC$) are congruent, as indicated by the tick marks.

2. Properties of Isosceles Trapezoids: In an isosceles trapezoid, the consecutive angles between a pair of parallel sides are supplementary. This means: $\angle A + \angle D = 180^\circ \quad \text{and} \quad \angle B + \angle C = 180^\circ$

3. Given Angle: The measure of $\angle A$ is provided as $115^\circ$.

4. Calculate $\angle D$: Since $\angle A$ and $\angle D$ are consecutive angles along the parallel sides $AB$ and $CD$, they must add up to $180^\circ$. $\angle D = 180^\circ - 115^\circ = 65^\circ$

Conclusion:

The measure of $\angle ADC$ in quadrilateral $ABCD$ is $65^\circ$.

The correct answer is: 65°

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Related Questions:

1. What are the properties of an isosceles trapezoid?
2. How do you calculate supplementary angles in a quadrilateral?
3. What is the sum of the interior angles in any quadrilateral?
4. How can we find unknown angles in an isosceles trapezoid?
5. What other types of quadrilaterals have pairs of supplementary angles?

Tip: In isosceles trapezoids, the non-parallel sides are always equal, and angles along each parallel side are supplementary.