Please tell how to solve Q 26

Dear student,

Here AB,AD and BD are side of a triangle and all the sides are equal as per question.
This means that triangle is equilateral triangle and each angle is of 60 deg .
$$\begin{gathered} Now \angle ADC + \angle ADB = 180° \\ \angle ADB= 60° as the triangle is equilateral triangle . \\ \Rightarrow \angle ADC =180° - 60° = 120°.........1 \\ Now in △ADC , AD= DC\{ given \} \\ So the triangle is isosceles triangle . \\ i.e\angle DAC =\angle ACD .........2 \\ Let the angle be y°. \\ Now we know that sum of all the angle of triangle is 180°. \\ or,\angle ACD+\angle ADC+\angle DAC =180° \\ or,\angle ADC+2y=180° \\ or,120° + 2y =180° \{by eq 1 and 2\} \\ \Rightarrow 2y=60° \\ \Rightarrow y=30° \\ Now \angle ADC : \angle C = 120°:30° = 4:1 \\ Hence proved . \\ Hope this would have cleared your doubt . \end{gathered}$$
Regards