the angles of pentagon are in the ratio 3:4:5:7:8 what is the value of the largest angle in degrees
Answers
The value of the largest angle is 160°
Given:
The ratio of angles of pentagon are 3:4:5:7:8
To find:
The value of largest angle in degrees
Solution:
Pentagon: A pentagon is a five-sided geometrical shape with five angles. "Penta" stands for five, and "gon" stands for angle. One of the types of polygons is the pentagon. A regular pentagon's interior angles add up to 540 degrees.
Let the angles of the Pentagon be 3x, 4x, 5x, 7x and 8x.
Let 'n' be the number of sides.
In a regular Pentagon, sum of interior angles = (2n - 4) × 90°
= ( 2 × 5 - 4) × 90°
= 6 × 90°
= 540°
According to the ques
=> 3x + 4x + 5x + 7x + 8x = 540°
=> 27x = 540°
=> x = 540° / 27
=> x = 20°
The interior angles of the given Pentagon -
1) 3x = 3 × 20° = 60°
2) 4x = 4 × 20° = 80°
3) 5x = 5 × 20° = 100°
4) 7x = 7 × 20° = 140°
5) 8x = 8 × 20° = 160°
Hence, the value of the largest angle is 160°
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