Chapter 6 Rectilinear Figures Ex 6.2

Rajasthan Board RBSE Class 9 Maths Solutions Chapter 6 Rectilinear Figures Ex 6.2

Question 1.
A regular polygon has 8 sides, then
(i) Find the sum of the exterior angles.
(ii) Find the measure of each exterior angles.
(iii) Find the sum of all interior angles.
(iv) Find the measure of each interior angle.
Solution.
(i) The sum of all exterior angles having 8 sides = 360°
(ii) Each exterior angles of an octagon

Question 2.
The sum of the interior angles of a polygon is 2160°, find the number of sides in the polygon.
Solution.
The sum of the interior angles of a polygon = (2n – 4) x 90°
⇒ 2160° = 180°n – 360°
⇒ 2160° + 360° = 180°n

Hence, number of sides of required polygon is 14.

Question 3.
Can there exist a regular polygon whose interior angle is 137°?
Solution.
It is given that the measure of each interior angle of a regular polygon = 137° (if possible)
Suppose number of sides of the polygon = n
Sum of all then exterior angles = 360°
⇒ n x 43 = 360°

Hence, a regular polygon having a measure of each interior angle 137° cannot exist.

Question 4.
In the given figure, find the measure of ∠CED.

Solution.
In ∆ACE
∠A + ∠C + ∠E = 180°
(by angle sum property of a triangle)
⇒ 31° + 75° + ∠E = 180°
⇒ ∠E = 180° – 106°
⇒ ∠E = 74°