Sum of Interior Angles in a Polygon Find the value of x:
Answers
Answer:
Q.1. x=45°
Q.2. x=150°
Q.3. x=120°
Step-by-step explanation:
formula for calculating the sum of interior angles in polygon is:
(n-2)×180°
(where n is the number of sides)
Q2.
n=4. sum =x +2x+2x+3x= (4-2)× 180°
8x =360°
x=45°
Q3.
n=6. sum =x +x+x+90+90+90= (6-2)× 180°
3x+270=720°
3x=720-270
x=450÷3
x=150°
Q4.
n=5. sum =x +2x+2x+90+90= (5-2)× 180°
3x+180=540°
3x=540-180
x=360÷3
x=120°
Solution :-
(2)
→ Sum of interior angles of a regular polygon with n - sides = (n - 2) * 180°
So,
→ n = 4
then,
→ (3x + 2x + 2x + x) = (4 - 2) * 180°
→ 8x = 2 * 180°
→ 4x = 180°
→ x = 45°
(3)
→ n = 6
So,
→ (x + x + x + 90° + 90° + 90°) = (6 - 2) * 180°
→ 3x + 270° = 4 * 180°
→ 3(x + 90°) = 4 * 180°
→ x + 90° = 4 * 60°
→ x + 90° = 240°
→ x = 240° - 90°
→ x = 150°
(4)
→ n = 5
So,
→ (x + 2x + 2x + 90° + 90°) = (5 - 2) * 180°
→ 5x + 180° = 3 * 180°
→ 5(x + 36°) = 3 * 180°
→ x + 36° = 3 * 36°
→ x + 36° = 108°
→ x = 108° - 36°
→ x = 72°
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