Question

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Answer 1

The sum of interior angles of a Pentagon= 180(n-2)
                                                                 = 180(5-2)
                                                                 = 180*3=540°
let the center of the circle of the circle be O
join BO , CO ,DO
AO and BO are radii of the circle
∠OAB=∠OBA=X
BO and CO are radii of the circle
∠OBC=∠OCB=Y
similarly,∠OCD=∠ODC=Z
              ∠ODE=∠OED=M
∠OAB+∠ABC+∠BCD+∠CDE+∠DEO=540
X+(X+Y)+(Y+Z)+(Z+M)+M=540
[∵∠ABC=∠OBA+∠OBC]       [∵∠CDE=∠ODC+∠ODE]
2X+2Y+2Z+2M=540
2(X+Y+Z+M)=540
X+Y+Z+M=540/2 = 270
(X+Y)+(Z+M)=270
=>∠ABC+∠CDE=270
∴∠ABC+∠CDE=270