Rectilinear Figures
ICSE · Class 9 · Mathematics
Flashcards for Rectilinear Figures — ICSE Class 9 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Get startedSolve: The sum of the interior angles of a polygon is five times the sum of its exterior angles. Find the number of sides.
Answer
Step 1: Let the number of sides be n. Step 2: Sum of interior angles = (2n - 4) right angles = (2n - 4) × 90°. Step 3: Sum of exterior angles = 360°. Step 4: Given, (2n - 4) × 90° = 5 × 360°. Step 5: …
Solve: One angle of an eight-sided polygon is 100° and the other seven angles are equal. Find each equal angle.
Answer
Step 1: For an 8-sided polygon, sum of interior angles = (2n - 4) × 90°. Step 2: Substitute n = 8: (16 - 4) × 90° = 12 × 90° = 1080°. Step 3: Remaining sum after one 100° angle = 1080° - 100° = 980°.
Solve: In pentagon ABCDE, AB is parallel to ED and angle B = 140°. If angle C : angle D = 5 : 6, find angle C and angle D.
Answer
Step 1: Since AB is parallel to ED, angle A + angle E = 180°. Step 2: Let angle C = 5x and angle D = 6x. Step 3: Sum of angles of a pentagon = (2 × 5 - 4) × 90° = 540°. Step 4: So, (angle A + angle E)…
Solve: In a pentagon, angle A = 110°, angle B = 140°, and angle D = angle E. The sides AB and DC produced meet at right angle. Find angle BCD and angle E.
Answer
Step 1: Since AB and DC produced meet at right angle, the outside angle at the meeting point is 90°. Step 2: From angle B = 140°, the adjacent angle made on the straight line gives 180° - 140° = 40°.
Solve: The sum of the interior angles of a doubly re-entrant heptagon is found by dividing it into triangles. Find the sum of its angles.
Answer
Step 1: A heptagon has 7 sides. Step 2: When divided into triangles, the figure gives 5 triangles. Step 3: Sum of angles of one triangle = 180°. Step 4: Total sum = 5 × 180° = 900°. Step 5: Check with…
When do you use the formula for the sum of interior angles of a polygon? Apply it to a 6-sided polygon.
Answer
Use this formula when the total inside angle sum of a polygon is needed: Sum of interior angles = (2n - 4) right angles = (2n - 4) × 90°. For n = 6: Step 1: (2 × 6 - 4) × 90° Step 2: (12 - 4) × 90° = …
When do you use the formula for the sum of exterior angles of a polygon? Show it for any polygon.
Answer
Use this formula when the sides are produced in order and the total outside turning angle is needed. Sum of exterior angles = 4 right angles = 360°. Example: For any polygon, the exterior angles taken…
Find the number of sides of a regular polygon if each exterior angle is 45°.
Answer
Step 1: Use the formula n = 360/x. Step 2: Here x = 45°. Step 3: n = 360/45 = 8. Step 4: Check: 8 × 45° = 360°. Answer: The polygon has 8 sides.
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