Solved Questions on Practical Geometry
1. What is the value of an exterior angle ∠GFX of the given figure?
a) 30°
b) 40°
c) 50°
d) 40°
Answer: b) 40°
Explanation: The figure is a regular nonagon.
Number of sides (n) = 9
Measure of each exterior angle in a regular polygon of n sides = 360°/n
Measure of each exterior angle in a regular nonagon = 360°/9
= 40°
2. What is the sum of the interior angles of the given figure?
a) 950°
b) 980°
c) 1050°
d) 1080°
Answer: d) 1080°
Explanation: The figure is a regular octagon.
Number of sides (n) = 8
Sum of interior angles in a regular polygon of n sides = (n − 2) × 180°
Sum of interior angles in a regular octagon = (8 − 2) × 180°
= 6 × 180°
= 1080°
3. What is the value of each interior angle of the given figure?
a) 118.57°
b) 126.57°
c) 128.57°
d) 136.57°
Answer: c) 128.57°
Explanation: The figure is a regular heptagon.
Number of sides (n) = 7
Each interior angle in a regular polygon of n sides = (n − 2) × 180°/n
Each interior angle in a regular heptagon = (7 − 2) × 180°/7
= 5 × 180°/7
= 900°/7
= 128.57°
4. How many diagonals are present in the polygon ABCDEF?
a) 3
b) 6
c) 9
d) 12
Answer: c) 9
Explanation: The polygon ABCDEF is a regular hexagon.
Number of sides (n) = 6
Number of diagonals in a regular polygon of n sides = n (n − 3)/2
Number of diagonals in a regular hexagon = 6 (6 − 3)/2
= 6 × 3/2
= 18/2
= 9
5. What is the sum of angles a, b, c and d?
a) 344°
b) 354°
c) 364°
d) 374°
Answer: b) 354°
Explanation: Using the figure,
Sum of exterior angles in a polygon (Quadrilateral) = 360°
a + b + c + 106° = 360°
a + b + c = 360° − 106°
a + b + c = 254°
Interior angle + exterior angle = 180°
x + 106° = 180°
x = 180° − 106°
x = 74°
Sum of all the angles within a quadrilateral = 360°
d + 62° + x + 124° = 360°
d + 62° + 74° + 124° = 360°
d + 260° = 360°
d = 360° − 260°
d = 100°
Sum of angles a, b, c and d = a + b + c + d
= 254° + 100°
= 354°
