In the given figure,sides of a regular hexagon are produced Prove that 1+ 2+ 3+ 4+ 5+ 6=360 degrees - Maths - Lines and Angles

Question

In the given figure,sides of a regular hexagon are produced Prove
that <1+<2+<3+<4+<5+<6=360 degrees 
​

Lovina Kansal · Accepted Answer

Dear student
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/images/1%28122%29%20png">
Let ABCDEF is a regular hexagon
Number of sides=n=6Now, sum of interior angles=n-2×180°=6-2×180°=4×180°=720°Measure of each interior angle=720°6=120°At point A,∠FAB+∠BAL=180°    (Linear pair)120°+∠BAL=180°∠BAL=60°Similarly, we get∠CBM=∠DCN=∠EDO=∠FEP=∠AFQ=60°Now,∠BAL+∠CBM+∠DCN+∠EDO+∠FEP+∠AFQ=60°+60°+60°+60°+60°+60°⇒∠BAL+∠CBM+∠DCN+∠EDO+∠FEP+∠AFQ=360°Hence proved
Regards

In the given figure,sides of a regular hexagon are produced.Prove that <1+<2+<3+<4+<5+<6=360 degrees.​

In the given figure,sides of a regular hexagon are produced.Prove that <1+<2+<3+<4+<5+<6=360 degrees.