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If an angle of a parallelogram is two-third of its adjacent angle, then find the smallest angle of the parallelogram.
- a)36
- b)120
- c)72
- d)90
Correct answer is option 'C'. Can you explain this answer?
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To find the smallest angle of a parallelogram, we can use the given information that one angle is two-thirds of its adjacent angle. Let's assume that the adjacent angle is x degrees.
Let's break down the solution into steps:
Step 1: Identify the given information
- One angle of the parallelogram is two-thirds of its adjacent angle.
Step 2: Set up an equation
Let the adjacent angle be x degrees. According to the given information, one angle is two-thirds of its adjacent angle. So, the other angle can be expressed as (2/3)x degrees.
Step 3: Use the properties of a parallelogram
In a parallelogram, opposite angles are equal. Therefore, the opposite angle to the angle measuring (2/3)x degrees is also (2/3)x degrees.
Step 4: Find the sum of all angles in a parallelogram
The sum of all angles in a parallelogram is equal to 360 degrees. So, we can set up an equation:
x + (2/3)x + x + (2/3)x = 360
Step 5: Solve the equation
To solve the equation, we can simplify it:
(3/3)x + (2/3)x + (3/3)x + (2/3)x = 360
(10/3)x = 360
x = (360 * 3) / 10
x = 108
Step 6: Find the smallest angle
The smallest angle of the parallelogram is (2/3)x degrees. Substituting the value of x, we have:
(2/3) * 108 = 72
Therefore, the smallest angle of the parallelogram is 72 degrees. Hence, the correct answer is option C.
Let's break down the solution into steps:
Step 1: Identify the given information
- One angle of the parallelogram is two-thirds of its adjacent angle.
Step 2: Set up an equation
Let the adjacent angle be x degrees. According to the given information, one angle is two-thirds of its adjacent angle. So, the other angle can be expressed as (2/3)x degrees.
Step 3: Use the properties of a parallelogram
In a parallelogram, opposite angles are equal. Therefore, the opposite angle to the angle measuring (2/3)x degrees is also (2/3)x degrees.
Step 4: Find the sum of all angles in a parallelogram
The sum of all angles in a parallelogram is equal to 360 degrees. So, we can set up an equation:
x + (2/3)x + x + (2/3)x = 360
Step 5: Solve the equation
To solve the equation, we can simplify it:
(3/3)x + (2/3)x + (3/3)x + (2/3)x = 360
(10/3)x = 360
x = (360 * 3) / 10
x = 108
Step 6: Find the smallest angle
The smallest angle of the parallelogram is (2/3)x degrees. Substituting the value of x, we have:
(2/3) * 108 = 72
Therefore, the smallest angle of the parallelogram is 72 degrees. Hence, the correct answer is option C.
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If an angle of a parallelogram is two-third of its adjacent angle, the...
Sum of 2 adjacent angle Is 180• then 2/3 × 180=72
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