Question

The alternate sides of any regular pentagon are produced to meet so as to form a star shaped figure. shown in the given figure.

Show that ∠x + ∠y + ∠z + ∠t + ∠u = 180°

Answer 1

Each interior angle of a regular pentagon = \(\frac{(5-2)\times180°}{5}\) = 108°

∴ Ext. ∠BAK = Ext.∠ABK= 180° – 108° = 72° 

∴ In ΔABK, \(x\) = 180° – (72° + 72°) 

= 180° – 144° = 36° 

Similarly, we can show u = t = y = z = 36° 

∴ ∠\(x\) + ∠y + ∠z + ∠t +∠u = 36° × 5 = 180°.