 ABCD is a quadrilateral with angle a = 160 degree, angle b =  80 degree and ab=bc=ad then find the value of angle c is

Let's analyze the given problem:

1. **Given Information:**
   - Quadrilateral \( ABCD \) has angles \( \angle A = 160^\circ \) and \( \angle B = 80^\circ \).
   - The sides \( AB = BC = AD \).

2. **Understanding the Shape:**
   Since \( AB = AD \), triangles \( \triangle ABD \) and \( \triangle BCD \) are isosceles triangles. Also, \( AB = BC \), indicating symmetry about line \( BD \).

3. **Calculating \( \angle D \):**
   Using the properties of quadrilaterals:
   \[
   \angle A + \angle B + \angle C + \angle D = 360^\circ
   \]
   Plugging in the values for \( \angle A \) and \( \angle B \):
   \[
   160^\circ + 80^\circ + \angle C + \angle D = 360^\circ
   \]
   \[
   \angle C + \angle D = 360^\circ - 240^\circ = 120^\circ
   \]

4. **Relation between \( \angle C \) and \( \angle D \):**
   Since \( \triangle BCD \) is isosceles, \( \angle B = \angle C \).

5. Therefore, the solution yields \( C=80^\circ

ABCD is a quadrilateral with angle a = 160 degrees, angle b = 80 degrees, and AB = BC = AD. Find the value of angle C.

This geometry problem asks you to find the value of angle C in quadrilateral ABCD, where angle A = 160°, angle B = 80°, and sides AB = BC = AD. Using the properties of isosceles triangles and the angle sum property of quadrilaterals, you can solve this step by step. Suitable for students in Grades 8-10.

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