Worksheet on Basic Geometrical Ideas for Class 6

Master geometry fundamentals with our basic geometrical ideas grade 6 printable practice questions. This foundational activity sheet teaches students about points, lines, angles and curves through construction activities and practical applications. Children will understand geometric concepts essential for advanced mathematical learning and spatial reasoning. Download free Class 6 basic geometrical ideas worksheet pdf, and build geometry foundations.

Solved Questions on Basic Geometrical Ideas

1. What is the value of ∠EBD?

a) 65°
b) 75°
c) 105°
d) 115°

Answer: b) 75°

Explanation: In the given figure, ∠EBD is marked.

In triangle ABC, 

∠ABC + ∠BAC + ∠ACB = 180° (Sum of its three angles in a triangle is 180°)
⇒ ∠ABC + 60° + 45° = 180°
⇒ ∠ABC + 105° = 180°
⇒ ∠ABC = 180° − 105°
⇒ ∠ABC = 75°   

∠EBD = ∠ABC = 75° (Vertically Opposite Angle)

2. What is the value of x°?

a) $\frac{\frac{\mathrm{289°}}{}}{\frac{7}{}}$
b)$\frac{\frac{\mathrm{290°}}{}}{\frac{7}{}}$
c)$\frac{\frac{\mathrm{285°}}{}}{\frac{7}{}}$
d) $\frac{\frac{\mathrm{285°}}{}}{\frac{8}{}}$

Answer:$\frac{\frac{\mathrm{285°}}{}}{\frac{7}{}}$

Explanation: (x + 30)° +  (x − 20)° +  2x° +  (x + 45)° +  (x − 5)° +  (x + 25)° = 360°

⇒ 7x° + 75° = 360°
⇒ 7x° = 360° − 75°
⇒ 7x° = 285°
⇒ x° = $\frac{\frac{\mathrm{285°}}{}}{\frac{7}{}}$

3. What is the length of OH if the length of AE is 9.39 cm?

a) 4.5 cm
b) 4.7 cm
c) 4.9 cm
d) 4.95 cm

Answer: b) 4.7 cm

Explanation: Length of AE (Diameter) = 9.39 cm

Length of OH (Radius)
= Diameter/2
= AE/2
= 9.39 cm/2
= 4.695 cm
= 4.70 cm (Round off)

4. What is the value of x if ∠ABC = 55°, ∠CAB = 32° and obtuse angle AED = 115°?

a) 22°
b) 26°
c) 28°
d) 30°

Answer: c) 28° 

Explanation: Given: ∠ABC = 55°, ∠CAB = 32° and ∠AED =115°

Exterior angle of a triangle is the sum of the measure of the two interior angles that are opposite to it. 

In △ABC, 

∠ACD = ∠ABC + ∠CAB
⇒ ∠ACD = 55° + 32°
⇒ ∠ACD = 87°

 In △CDE,

∠EDC + ∠ECD = ∠AED     (∠ACD and ∠ECD is the same angle)
⇒ x + 87° = 115° 
⇒ x = 115° − 87°
⇒ x = 28°

5. What is the radius of the circular field if the circumference is 363 metres?

a) 52.25 m
b) 52.75 m
c) 57.25 m
d) 57.75 m

Answer: d) 57.75 m

Explanation: Circumference of the circle = 363 metres

⇒ 2 × ²²⁄₇ × r = 363 
⇒ r = 363 × ¹⁄₂ × ⁷⁄₂₂
⇒ r = 57.75 m