Angles In Polygons And Parallel Lines
खेलकर सीखें
इन सवालों के जवाब देकर एनर्जी कमाएं, फिर मछली पकड़ें और घूमें। कोई अकाउंट नहीं चाहिए।
लेसन नोट्स
Basic Angle Properties
- Angles around a point sum to 360°.
- Angles on a straight line sum to 180°.
- Vertically opposite angles are equal when two lines intersect.
- Interior angles of a triangle sum to 180°.
- Interior angles of a quadrilateral sum to 360°.
- In an isosceles triangle, base angles are equal.
- In an equilateral triangle, each angle is 60°.
Angles in Polygons
- A polygon with n sides has interior angle sum = 180^\circ \times (n-2).
- Exterior angles of any polygon sum to 360°.
- For a regular polygon: interior angle = \frac{180(n-2)}{n}, exterior angle = \frac{360}{n}.
- Interior and exterior angles at a vertex sum to 180°.
- To find missing angles in a polygon, subtract known angles from the sum.
- If given interior angle of a regular polygon, solve \frac{180(n-2)}{n} = \text{angle} to find n.
Interior and exterior angles of a polygon
Angles in Parallel Lines
- Corresponding angles (F-shape) are equal.
- Alternate angles (Z-shape) are equal.
- Co-interior angles (C-shape) sum to 180°.
- Vertically opposite angles also apply in parallel line problems.
- Always give reasons (e.g., 'corresponding angles on parallel lines are equal').
Corresponding angles (F-shape)
Common Regular Polygons
- Equilateral triangle (3 sides): interior 60°, exterior 120°.
- Square (4 sides): interior 90°, exterior 90°.
- Regular pentagon (5 sides): interior 108°, exterior 72°.
- Regular hexagon (6 sides): interior 120°, exterior 60°.
- Regular octagon (8 sides): interior 135°, exterior 45°.
- Regular decagon (10 sides): interior 144°, exterior 36°.
स्लाइड्स
Sign up free to view the lesson slides
Step through every slide for this topic — plus flashcards and revision notes — with a free account.
प्रैक्टिस सवाल
फ्री प्रीव्यू — 45 में से 8 सवाल। सभी देखने के लिए साइन अप करें।
1.What is the sum of the interior angles of a pentagon?
Easy- A540°
- B360°
- C720°
- D180°
2.In a regular polygon, each interior angle is 150°. How many sides does the polygon have?
Medium- A12
- B10
- C15
- D8
3.Angles on a straight line add up to:
Easy- A180°
- B360°
- C90°
- D270°
4.In the diagram, two parallel lines are cut by a transversal. One angle is 70°. What is the size of the alternate angle?
Easy- A70°
- B110°
- C180°
- D90°
5.A regular polygon has 72 sides. Find the size of an interior angle.
Medium- A175°
- B170°
- C180°
- D165°
6.In a regular polygon, the interior angle is 11 times the exterior angle. Find the number of sides.
Hard- A24
- B22
- C20
- D30
7.The diagram shows a regular pentagon. Find the size of angle x.
Medium- A36°
- B72°
- C108°
- D54°
8.Vertically opposite angles are:
Easy- Aequal
- Bsupplementary
- Ccomplementary
- Dnone of the above
Unlock all 45 questions & more
इस टॉपिक के हर सवाल, स्लाइड्स, फ्लैशकार्ड और रिवीज़न नोट्स देखने के लिए फ्री अकाउंट बनाएं।