Question

porve it that the sum is 180
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Answer 1

Answer:

Step-by-step explanation:

Angle B happens to be congruent with itself. Therefore, the sum of angles A, B, and C must be equal to the sum of the angles B, E, and F. And since the sum of angles A, B, and C is known to be 180, then the sum of angles B, E, and F must also be 180.

Answer 2

Given :

A, B, C, D, E are points on circle.

To prove :

∠A+∠B+∠C+∠D+∠E = 180°

Construction :

Join the points A, B, C, D, E as shown in figure and name the angles.

Proof :

• Angles in the same segment of a circle are equal.

For chord CD,

⇒ ∠1=∠2=∠3...[ 1 ]

For chord DE,

 ⇒∠4=∠5=∠6...[ 2 ]

For chord EA,

⇒ ∠7=∠8=∠9...[ 3 ]

For chord AB,

⇒ ∠10=∠11=∠12...[ 4 ]

For chord BC,

⇒ ∠13=∠14=∠15...[ 5 ]

Now, consider 

∠DEB,∠EBC,∠BCD and ∠CDE.

Since EBCD is a quadrilateral

we all know that the sum of the angle in a quadrilateral is 360°.

:⟶∠DEB+∠EBC+∠BCD+∠CDE=360°

:⟶(∠3+∠14)+(∠5+∠1)+(∠10+∠8+∠6)+(∠13+∠11+∠9)=360

:⟶∠3+∠14+∠5+∠1+∠10+∠8+∠6+∠13+∠11+∠9=360°

From [ 1 ] , [ 2 ] , [ 3 ] , [ 4 ] and [ 5 ]

:⟶∠A+∠E+∠B+∠A+∠D+∠C+∠B+∠E+∠D+∠C=360°

:⟶2(∠A+∠B+∠C+∠D+∠E)=360°

:⟶∠A+∠B+∠C+∠D+∠E=180°

Hence proved !