Question

Find the sum of angles -1, 2, 3, 4, 5 and 6. ​

Answer 1

sum of the angles of 123456 360 because these are of angle of two triangles and each triangle has the angle of 180 total sum

Answer 2

4

Consider a quadrilateral ABCD.

Then, ∠A+∠B+∠C+∠D=360

To prove this, we join A and C, i.e. we draw the diagonal AC.

In △ABC,

∠CAB+∠ABC+∠BCA=180

[Sum of all angles of a triangle is 180

In △ACD,

∠CAD+∠ADC+∠DCA=180

[Sum of all angle of a triangle is 180

Adding (1) and (2), we get,

(∠CAB+∠ABC+∠BCA)+(∠CAD+∠ADC+∠DCA)=180

+180

∠ABC+∠ADC+(CAB+CAD)+(BCA+DCA)=360

∠ABC+∠ADC+∠BAD+∠BCD=360

∠A+∠B+∠C+∠D=360

That is, the sum of all angles of a quadrilateral is 360

o

=4×90

o

, i.e. 4 right angles.