Question

How many sides does a regular polygon have if the measure
of each of its interior angle is 156°

​

Answer 1

Answer:

Hope it helps!! Mark this answer as brainliest if u found it useful.

Step-by-step explanation:

Let the polygon be n-sided.

Given that Each interior angle measures 156°

So, ( n-2 ) × 180 / n = 156

=> 180n - 360 = 156n .

=> 180n - 156n = 360

=> 24 n = 360

=> n = 360/24 = 180/12 = 90/6 = 15 .

=> n = 15 sides.

Therefore ,The polygon with each interior angle 156° has 15 sides.

Answer 2

Solution :-

We know that, for a polygon of total n sides,

• Sum of all interior angles = (n - 2) * 180° .

So, let us assume that, the given polygon has total n sides .

Then,

→ Sum of all interior angles / Total sides = 156°

→ (n - 2) * 180° / n = 156°

→ 180n - 360° = 156n

→ 180n - 156n = 360°

→ 24n = 360°

→ n = 15 (Ans.)

Hence, the given polygon has total 15 sides .

Learn more :-

In the figure along side, BP and CP are the angular bisectors of the exterior angles BCD and CBE of triangle ABC. Prove ∠BOC = 90° - (1/2)∠A .

https://brainly.in/question/32333207