Question

In a regular polygon of n sides, the measure of each internal angle is 2n right angles.

Answer 1

Answer:

We know that if a polygon has 'n' sides, then it is divided into (n – 2) triangles. We also know that, the sum of the angles of a triangle = 180°. Therefore, the sum of interior angles of a polygon having n sides is (2n – 4) right angles. Thus, each interior angle of the polygon = (2n – 4)/n right angles.

Step-by-step explanation:

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Answer 2

Given statement "In a regular polygon of n sides, the measure of each internal angle is 2n right angles" is FALSE as  the measure of each internal angle is 2(n - 2)/n   Right angles

Given :

In a regular polygon of n sides, the measure of each internal angle is 2n right angles.

To Find:

Given Statement is True or False

Solution:

• A Regular polygon with n sides will have where  n ≥ 3  
• n Exterior angles
• n Interior angles
• As Polygon is Regular
• All interior angles will be equal
• All exterior  angles will Equal
• Sum of Adjacent interior and exterior angle = 180° ( Linear Pair)
• Sum of All the exterior angles of a polygon is 360°
• Right angle measures 90°

Step 1 :

Find Exterior angle

360°/n

Step 2 :

Find Interior angle

180° - 360°/n

= 180°(1 - 2/n)

= 180° (n - 2)/n

= 2 x 90° (n - 2)/n

= 2(n - 2)/n   x 90°

= 2(n - 2)/n   Right angles

In a regular polygon of n sides, the measure of each internal angle is 2(n - 2)/n   Right angles

Hence Given statement "In a regular polygon of n sides, the measure of each internal angle is 2n right angles" is FALSE

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