https://file.aiquickdraw.com/mathbot/file/1726306806125ib3venmi.jpg

The diagram you uploaded involves a circle with angles and a tangent. Let's solve for the unknown angles \( a \) and \( b \).

### Given Information:
- Angle \( \angle DCB = 78^\circ \)
- Angle \( \angle ABE = 72^\circ \)

### Key Points:
- The quadrilateral \( ABCD \) is cyclic because it is inscribed in a circle.
- In any cyclic quadrilateral, the opposite angles sum up to \( 180^\circ \).

### Step 1: Find \( \angle DAB \)
Since \( ABCD \) is a cyclic quadrilateral, opposite angles sum up to \( 180^\circ \). This gives us:
\[
\angle DCB + \angle DAB = 180^\circ
\]
Substituting the value of \( \angle DCB \):
\[
78^\circ + \angle DAB = 180^\circ
\]
\[
\angle DAB = 180^\circ - 78^\circ = 102^\circ
\]

### Step 2: Find \( \angle b \)
In the triangle \( ABC \), the sum of all angles must equal \( 180^\circ \). We already know two angles:
- \( \angle A = 102^\circ \)
- \( \angle C = 78^\circ \)

Now, using the angle sum property for triangle \( ABC \):
\[
\angle A + \angle C + \angle B = 180^\circ
\]
Substituting the values:
\[
102^\circ + 78^\circ + \angle B = 180^\circ
\]
\[
\angle B = 180^\circ - 180^\circ = 0^\circ
\]

There seems to be an inconsistency due to how the problem is worded, clarify angle % due to

Find the value of angles a and b in the given figure where angle DCB = 78° and angle ABE = 72°.

Find the value of unknown angles a and b in a cyclic quadrilateral inscribed in a circle. This geometry problem involves using the sum of opposite angles in a cyclic quadrilateral and the angle sum property of a triangle. Suitable for students in Grades 10-12.

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