Calculate all the angles of a parallelogram if one of its angles is tw...
Introduction:
A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. The sum of the angles in a quadrilateral is always 360 degrees. In this question, we are given that one of the angles in the parallelogram is twice its adjacent angle, and we need to find the measures of all the angles.
Step 1: Understanding the given information:
Let's assume that the measure of one of the angles in the parallelogram is x degrees. According to the given information, one of the angles is twice its adjacent angle. So, the measure of the adjacent angle can be represented as 2x degrees.
Step 2: Identifying the properties of a parallelogram:
In a parallelogram, opposite angles are equal. Therefore, the opposite angle to the angle with measure x degrees will also be x degrees.
Step 3: Calculating the measures of the remaining angles:
Since opposite angles are equal, the opposite angle to the angle with measure 2x degrees will also be 2x degrees.
Now, we can use the fact that the sum of the angles in a quadrilateral is 360 degrees. So, we can write the equation as:
x + x + 2x + 2x = 360
Step 4: Solving the equation:
Simplifying the equation, we have:
6x = 360
Dividing both sides of the equation by 6, we get:
x = 60
Step 5: Finding the measures of all the angles:
Now that we have the value of x, we can substitute it back into the expressions we derived earlier to find the measures of all the angles.
The measure of the angle with measure x degrees is 60 degrees.
The measure of the adjacent angle is 2x degrees, which is 120 degrees.
The measure of the opposite angle to the one with measure x degrees is also x degrees, which is 60 degrees.
The measure of the opposite angle to the one with measure 2x degrees is also 2x degrees, which is 120 degrees.
Conclusion:
In conclusion, the measures of all the angles in the parallelogram are as follows:
- One angle measures 60 degrees.
- The adjacent angle measures 120 degrees.
- The opposite angle to the one with measure 60 degrees also measures 60 degrees.
- The opposite angle to the one with measure 120 degrees also measures 120 degrees.
To make sure you are not studying endlessly, EduRev has designed Class 9 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 9.