Selina Concise Class 6 Math Chapter 26 Polygons Exercise 26A Solution
EXERCISE 26A
(1) State, which of the following are polygons:
Ans: (ii) and (iii)
(2) Find the sum of interior angles of a polygon with:
(i) 9 sides: (2n – 4) × 90o
= [(2 × 9) – 4] × 90o
= (18 – 4) × 90o
= 14 × 90o = 1260o
(ii) 13 sides: (2n – 4) × 90o
= [(2 × 13) – 4] × 90o
= (26 – 4) × 90o
= 22 × 90o = 1980o
(iii) 16 sides: (2n – 4) × 90o
= [(2 × 16) – 4] × 90o
= (32 – 4) × 90o
= 28 × 90o = 2520
(3) Find the number of sides of a polygon, if the sum of its interior angles is:
Therefore it is not possible to have a polygon.
(5) (i) (2n – 4) × 90o
= [(2 × 6) – 4] × 90o
= (12 – 4) × 90o
= 8 × 90o = 720o
Hence, the measure of each angle = (720o ÷ 6) = 120o
(ii) (2n – 4) × 90o
= [(2 × 8) – 4] × 90o
= (16 – 4) × 90o
= 12 × 90o
= 1080o
Hence, measure of each angle = (1080o ÷ 8) = 135o
(6) Let the all equal angles measure be xo, xo, xo and given one angle is 90o.
Then, 3xo + 90o = 360o
⇒ 3xo = (360 – 90)o
⇒3x = 270o
⇒ x = 90o
(7) Let the measure of each angles be 4x, 5x, 3x and 6x.
Then, 4x + 5x + 3x + 6x = 360o
⇒ 18x = 360o
⇒ x = 20o
Hence, measure of each angle is
(4x) = 4 × 20o = 80o
(5x) = 5 × 20o = 100o
(3x) = 3 × 20o = 60o
(6x) = 6 × 20o = 120o
(8) Let the other angles of a pentagon be x, x, x, x and given one angle measure is 120o.
Then, sum of interior angle of a pentagon = (4x + 120o)
But sum of interior angle of a pentagon = (2n – 4) × 90o
= [(2 × 5) – 4] × 90o
= (10 – 4) × 90o
= 6 × 90o = 540o
Then, 4x + 120o = 540o
⇒ 4x = 540o – 120o = 420o
⇒ x = 105o
(9) Let the angles of pentagon be 5x, 4x, 5x, 7x and 6x.
Sum of interior angles of a pentagon = (2n – 4) × 90o
= [(2 × 5) – 4] × 90o
= (10 – 4) × 90o
= 6 × 90o = 540o
Then, 5x + 4x + 5x + 7x + 6x = 540o
⇒ 27x = 540o
⇒ x = 20o
Measure of each angle of the pentagon,
(5x) = 5 × 20o = 100o
(4x) = 4 × 20o = 80o
(5x) = 5 × 20o = 100o
(7x) = 7 × 20o = 140o
(6x) = 6 × 20o = 120o
(10) Let the remaining angles be x, x, x, x and given two angles are 90o and 110o.
Then, x + x + x + x + 90 + 110 = (2n – 4) × 90o
⇒ 4x + 200o = [(2 × 6) – 4] × 90o
⇒ 4x + 200o = (12 – 4) × 90o
⇒ 4x + 200o = 8 × 90o
⇒ 4x = 720o – 200o
⇒ 4x = 520o
⇒ x = 130o