Question

two angles of hexagon are 150 degree each and rest of the angles are all equal. Find the measure of the remaning angles​

Answer 1

Answer:

54 diagonals

Step-by-step explanation:

Diagonal of any polygon is a segment obtained by joining 2 opposite ie non adjacent vertices.

=> in any polygon , every vertex is to be joined with (n-3) vertices. Because 2 adjacent & that vertex itself will always be reduced from the total no of vertices….

Hence, number of diagonals we get

= (n-3) +(n-3) +(n-3) + …… ntimes.

But, exactly half of the above given number of diagonals are repeating….

Like, in a pentagon, if vertices are 1,2,3,4,5

Then joining vertices by following way..

(1, 3)(1,4), (2,4)(2,5), (3,1)(3,5), (4,1)(4,2), (5,2)(5,3)

we get (5–3) + (5–3) + ……. 5 times

= 2*5= 10 segments in which exactly half will be repeated ones.

So, no of diagonals = 10÷2 = 5

So, Formula: no of diagonals = {(n-3)*n}÷ 2

Now, in the above question, measure of each angle of a regular polygon = 150°

=> (n-2)*180° /n = 150°

=> 180n - 150n = 360

=> 30n = 360

=> n = 12

=> given regular polygon is a 12 sided regular polygon.

So, number of diagonals = {(12–3)*12}÷2

= (9 *12)/2 = 108/2

= 54 diagonals

Answer 2

Answer:

54 diagonals is the answer