Question

Construct an angle ABC with B = 135 degree and arms AB =
135 degree and arms AB = BC = 4cm. At point
C, make another angle 135 degree (ZC = 135 degree) with arm CD 4cm.
Continue this process and find if a closed figure is obtained.​

Answer 1

Given :-

• ∠ABC = 135°
• AB = 4 cm = BC = 4 cm .
• CD = 4 .
• ∠C = 135°

Answer :-

we know that,

• interior angle of a regular polygon = (n - 2)180°/n .

given that, all angles will be 135° and all side measure are 4 cm .

so, let n sides formed a regular polygon,

then,

→ (n - 2)180/n = 135

→ 180n - 360 = 135n

→ 180n - 135n = 360

→ 45n = 360

→ n = 8 .

we can conclude that, a octagon will be obtained in this process .

Answer 2

Given :  Construct an angle ABC with B = 135 degree and arms AB = 4 cm then BC = 4c m then angle = 135 degree

To Find :  

Solution:

This process is making of  a regular polygon

Equal sides

equal angles

Regular polygon possible if  exterior angle is a divisor of 360°

here exterior angle = 180° - 135° = 45°

Number of Sides =  360° / exterior angle

=   360° / 45°

= 8

Hence regular OCTAGON will be obtained.

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