Question

In the figure , ⏹️ABCD is divided into two triangles by drawing the diagonal AC . Every triangle has three angles. how many angles are there in the given figure ?
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Please Explain Step by step ​

Answer 1

As shown in \triangleACD,

angle1+ angle2+angle3= 180degree

As shown in \triangleABC,

angle4 +angle 5+angle6 = 180degree

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 = 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 180degree + 180degree = 360degree.

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