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  • 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 ∠A, ∠B, ∠C and ∠D amounts to

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 angles amounts to 180\degree + 180\degree = 360\degree.

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best_answer

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.

Posted by

seema garhwal

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