Question

DO THIS
1. Take any quadrilateral, say ABCD (Fig 34). 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 ZA, ZB, ZC and
Fig 34 A
ZD amounts to 180° + 180º = 360°
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Answer 1

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Answer 2

Answer:

Given, ABCD is a quedrilatera and AC is one of its diagonal .

Clearly, angle1+angle4= angleA

and angle 2+angle 5=angle C

also, diagonal AV divides quadrilateral ABCD into two traingles ∆ ABC and ∆ ADC.

we know that, the sum of all angles of a teaingle is 180°.

Therefore,

in ∆ABC,we have angle4+angle5+angle6=180°

in ∆ ACD,we have angle1+angle2+ angle 3=180°

angle1+angle2+angle3+angle4+angle5+angle6=180°+180°

=⟩(angle1+angle4)+(angle2+angle5)+(angle3+angle6)=360°

angleA+angleC+ angle D+ angleB{360°

Hence,the sum of the measures of AngleA,angleB,angleC and angleD is 360°.