Q1. Take any quadrilateral, say ABCD (Fig 3.4). Divide it into two triangles, by drawing a diagonal. You get six angles 1, 2, 3, 4, 5 and 6. Use the angle-sum property of a triangle and argue how the sum of the measures of and amounts to 180\degree + 180\degree = 360\degree.

Answers (1)

As shown in \triangleACD,

                                \angle 1 + \angle 2+\angle 3 = 180\degree

As shown in \triangleABC,

                               \angle 4 + \angle 5+\angle 6 = 180\degree

\angle A + \angle B +\angle C + \angle D= (\angle 1+\angle 4) +\angle 6 + (\angle 2+\angle 5) + \angle 3                 ( Since,  \angle A = (\angle 1+\angle 4),\angle B = \angle 6 ,\angle C = (\angle 2+\angle 5),

                                                                                                                                                                                       \angle D = \angle 3 )

\angle A + \angle B +\angle C + \angle D= (\angle 1+\angle 2 +\angle 3) + (\angle 4+\angle 5 + \angle 6)

                                                  = 180\degree + 180\degree

                                                 = 360\degree

Hence proved,  the sum of the measures of \angle A,\angle B,\angle C and
\angle D amounts to 180\degree + 180\degree = 360\degree.

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