Question

Find the sum of the interior angles of any quadrilateral, by dividing it into two triangles.

Answer 1

Step 1: Draw a quadrilateral and divide it into two triangles by joining two opposite vertex:

Step 2: Calculate the sum of all the angles of quadrilateral:

In $△ADC$, $\text{∠DAC+∠D+∠ACD = 180° (Angle sum property of triangle)}$

In $△ABC$, $\text{∠BAC+∠B+∠ACB = 180° (Angle sum property of triangle)}$

Adding both the equations,

$$\begin{gathered} \angle DAC+\angle D+\angle ACD+\angle BAC+\angle B+\angle ACB=180°+180° \\ (\angle DAC+\angle CAB)+\angle B+(\angle ACB+ACD)+\angle D=360° \\ \angle A+\angle B+\angle C+\angle D=360°(\angle DAC+CAB=\angle A,\angle ACB+\angle ACD=\angle C) \end{gathered}$$

Hence, the sum of all the angles of quadrilateral is $360°$.