Answer:
\(36^{\circ}\)
Step-by-step explanation:
We are given that BDC is straight.
BD=DA
AB=AC=DC
Let \(m\angle B=x\)
Then, \(m\angle B=m\angle C=x\)
Because AB=AC, angle made by two equal sides are equal.
Let \(m\angle ADC=y=m\angle CAD\)
\(m\angle A=m\angle BAD+m\angle CAD\)
\(m\angle BAD=m\angle B\)
\(m\angle A=x+y\)
In triangle ABC
\(m\angle B+m\angle A+m\angle C=180^{\circ}\) sum of angles of triangle
\(x+x+y+x=180^{\circ}\)
\(3x+y=180^{\circ}\)
\(m\angle ADC=m\angle B+m\angle BAD=x+x=2x\)
Exterior angle is equal to sum of two interior angles on the opposite side.
Substitute the values then we get
\(3x+2x=180^{\circ}\)
\(5x=180^{\circ}\)
\(x=\frac{180}{5}=36^{\circ}\)
Hence, the size of angle C=\(36^{\circ}\)
