the interior angles of pentagon are in the ratio 4:5:6:7:5 find each angle of the pentagon
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A Pentagon has 5 angles and 5 sides.
The total angle inside any polygon can be calculated with
(n - 2) × 180°
Where n is the number of sides. In this case it's 5.
So,
n - 2 = 5 - 2 = 3
And,
3 × 180° = 540°
So the total angle is 540 degree. Since the ratio of each angle is given,
Angle 1 = (4 × 540) ÷ 4 + 5 + 6 + 7 + 5
2160 ÷ 27 = 80°
Similarly,
Angle 2 is 100°
Angle 3 is 120°
Angle 4 is 140°
Angle 5 is 100°
The total angle inside any polygon can be calculated with
(n - 2) × 180°
Where n is the number of sides. In this case it's 5.
So,
n - 2 = 5 - 2 = 3
And,
3 × 180° = 540°
So the total angle is 540 degree. Since the ratio of each angle is given,
Angle 1 = (4 × 540) ÷ 4 + 5 + 6 + 7 + 5
2160 ÷ 27 = 80°
Similarly,
Angle 2 is 100°
Angle 3 is 120°
Angle 4 is 140°
Angle 5 is 100°
rohit876:
yes question is complete
please answerme
give me like 10 minutes. I'll try.
ok
A hexagon has 6 angles and 6 sides. So, using the formula, the total angle in the interior is 720°. A omplete anlgle is of 360°, and hexagon has 6 of them. So, the sum of total angles both inside and outside the hexagon is 360° × 6 =2160°. Of the 2160°, 720° are on the inside. And the rest, 1440 is on the outside.
(6x - 1) + (10x + 2) + (8x + 2) + (9x - 3) + (5x +4) + (12x + 6) = 1440.
50x + 10 = 1440
50x = 1430
x = (1430 ÷ 50) = 28.6
Now, you just have to substitute the value of 6 in each of the equations. And you'll get each of those exterior angles.
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