Question

Answer it correctly..... Iwill mark as brainiest

Answer 1

5) 180° cause the total sum of all angles of quadrilateral=360°. so remaining angle= 360-180= 180° .

6)Number of sides = 180- 108 = 72°

Number of sides= 360/72 = 5

Number of sides of the polygon = 5 sides.

Answer 2

(5) If sum of two angles of a quadrilateral is 180° then the sum of remaining two angles will be 180°

(6) A regular polygon, each angle of which is of 108° has 5 sides

Step-by-step explanation:

(5) We know that

Sum of all the angles of a quadrilateral is 360°

Therefore, if sum of two angles of a quadrilateral is 180° then the sum of remaining two angles will be

$=360^\circ-180^\circ$

$=180^\circ$

(6) We know that sum of all the interior angles of a n side regular polygon is given by

$S=(2n-4)\times 90^\circ$

Therefore, measure of each angle will be

$A=\frac{S}{n}=\frac{(2n-4)\times 90^\circ}{n}$

Here

$A=108^\circ$

Thus,

$108^\circ=\frac{(2n-4)\times 90^\circ}{n}$

$\implies 108^\circ n=180^\circ n-360^\circ$

$\implies 180^\circ n-108^\circ n=360^\circ$

$\implies 72^\circ n=360^\circ$

$\implies n=\frac{360}{72}$

$\implies n=5$

Hope this answer is helpful.

Know More:

Q: Find the number of sides of a regular polygon if the sum of its interior angle is 1)1260 2)1980 3)3420

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