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If the angles of a pentagon are in the ratio 1 : 3 : 6 : 7 : 10, then the smallest angle is:
- a)30°
- b)32°
- c)27°
- d)20°
Correct answer is option 'D'. Can you explain this answer?
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If the angles of a pentagon are in the ratio 1 : 3 : 6 : 7 : 10, then...
Suppose the angles of a pentagon are
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x°, 3x°, 6x°, 7x°, 10x°
But x° + 3x° + 6x° + 7x° + 10x° = (2x5 -4) x 90°
or 27x° = 6 x 90°
or x = 20°
Most Upvoted Answer
If the angles of a pentagon are in the ratio 1 : 3 : 6 : 7 : 10, then...
Given: The angles of a pentagon are in the ratio 1 : 3 : 6 : 7 : 10
To find: The smallest angle
Solution:
Let's assume the common ratio between the angles of the pentagon is x.
So, the angles can be written as:
1x, 3x, 6x, 7x, and 10x
According to the properties of a pentagon, the sum of the angles is equal to 540 degrees.
Therefore, we can write the equation as:
1x + 3x + 6x + 7x + 10x = 540
Combining like terms, we get:
27x = 540
Dividing both sides of the equation by 27, we find:
x = 20
Now, we can substitute the value of x back into the expressions for the angles:
1x = 1 * 20 = 20 degrees
3x = 3 * 20 = 60 degrees
6x = 6 * 20 = 120 degrees
7x = 7 * 20 = 140 degrees
10x = 10 * 20 = 200 degrees
Since we are looking for the smallest angle, the answer is 20 degrees (option D).
Therefore, the smallest angle of the pentagon is 20 degrees.
To find: The smallest angle
Solution:
Let's assume the common ratio between the angles of the pentagon is x.
So, the angles can be written as:
1x, 3x, 6x, 7x, and 10x
According to the properties of a pentagon, the sum of the angles is equal to 540 degrees.
Therefore, we can write the equation as:
1x + 3x + 6x + 7x + 10x = 540
Combining like terms, we get:
27x = 540
Dividing both sides of the equation by 27, we find:
x = 20
Now, we can substitute the value of x back into the expressions for the angles:
1x = 1 * 20 = 20 degrees
3x = 3 * 20 = 60 degrees
6x = 6 * 20 = 120 degrees
7x = 7 * 20 = 140 degrees
10x = 10 * 20 = 200 degrees
Since we are looking for the smallest angle, the answer is 20 degrees (option D).
Therefore, the smallest angle of the pentagon is 20 degrees.
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If the angles of a pentagon are in the ratio 1 : 3 : 6 : 7 : 10, then the smallest angle is:a)30°b)32°c)27°d)20°Correct answer is option 'D'. Can you explain this answer?
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