From the image, we can observe a circle with some labeled points and given angles. Here's the breakdown of the problem:

Key Points:

1. A, B, C, E are points on the circumference of the circle.
2. D is the intersection point of diagonals (or chords) $AC$ and $BE$ inside the circle.
3. Angle $\angle ADE = 70^\circ$, and angle $\angle BDC = 85^\circ$.
4. The task is to determine the missing angle (denoted by $?$).

Solution:

In such diagrams, the inscribed angles theorem applies:

• The measure of an inscribed angle subtended by the same arc is equal.
• The angles opposite each other in a quadrilateral inscribed in a circle are supplementary.

Step 1: Angle Relationships in the Circle

The two angles $\angle ADE$ and $\angle BDC$ subtend arcs in the circle. The missing angle is $\angle BAE$, which subtends the same arc as $\angle BDC$.

Step 2: Complementary Angles

Using the property of a circle:

• $\angle BAE = \angle BDC$.
• Therefore, $\angle BAE = 85^\circ$.

Final Answer:

The missing angle is $\mathbf{85^\circ}$.

Let me know if you'd like further clarification!

Here are 5 related questions to expand your understanding:

1. What is the sum of all angles in a quadrilateral inscribed in a circle?
2. How do you find angles subtended by the same chord of a circle?
3. What is the relationship between opposite angles in a cyclic quadrilateral?
4. How does the central angle relate to the inscribed angle in a circle?
5. Can you determine the arc measures in this circle based on the given angles?

Tip: In a circle, always check for relationships between arcs and the angles subtended by them to simplify the problem.