Question

Prove that the sum of the angles at the vertices of a five-pointed star (see Figure 120) equals 180 degrees.​

Answer 1

Answer:

Let BE intersects AC and AD at L and M respectively

Now, in ▲ MBD, by using exterior angle property ∠2 = ∠B +∠D (1)

Similarly, in ▲LCE, ∠1 = ∠C +∠E (2)

In ▲ALM, ∠A+∠1+∠2 = 180°

⇒ ∠A+∠C +∠E + ∠B +∠D = 180° (From Eqs. (1) and (2))

Or ∠ A+∠B +∠C +∠D +∠E = 180°

Note: In n point star sum of all the angles at its vertices is (n − 4)×180°.

Answer 2

Answer:

-17

Step-by-step explanation:

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