91Ó°ÊÓ

The given diagram is:

It is being given that $\stackrel{¯}{AD}â‰\dots \stackrel{¯}{AC}$.

The angles opposite to the equal sides are also equal.

As, $\stackrel{¯}{AD}â‰\dots \stackrel{¯}{AC}$, therefore, the angles opposite to the sidesAD and ACare also equal.

That implies,$∠ACD=∠ADC$ .

As the sum of the angles of the triangle is$180°$ .

Therefore, the sum of the angles of the triangle $ACD$is$180°$ .

Therefore, it can be obtained that:

$\begin{array}{c}∠DAC+∠ACD+∠ADC=180°\\ 36°+∠ADC+∠ADC=180°\\ 2∠ADC=180°−36°\\ 2∠ADC=144°\\ ∠ADC=\frac{144°}{2}\\ ∠ADC=72°\end{array}$

Therefore, the measure of the angle$∠ADC$ is $72°$.

It is also being given that$∠ADFâ‰\dots ∠CDF$.

Therefore,$∠ADF=∠CDF$ .

From the diagram it can be noticed that:

$∠ADC=∠ADF+∠CDF$.

Therefore, it can be obtained that:

$\begin{array}{c}∠ADC=∠ADF+∠CDF\\ 72°=∠ADF+∠ADF\\ 72°=2∠ADF\\ \frac{72°}{2}=∠ADF\\ 36°=∠ADF\end{array}$

Therefore, the measure of the angle$∠ADF$ is 18.

$m∠DAC=36$, so $m∠ADC=72°$ and $m∠ADF=36°$.