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What is the value of x if the measure of two adjacent angles of a parallelogram are 2x - 10 and 3x + 40?
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What is the value of x if the measure of two adjacent angles of a para...
Understanding Angles in a Parallelogram
In a parallelogram, adjacent angles are supplementary, meaning they add up to 180 degrees. Given the measures of two adjacent angles as 2x - 10 and 3x + 40, we can set up an equation to find the value of x.
Setting Up the Equation
- The sum of the angles:
- (2x - 10) + (3x + 40) = 180
- Simplifying this:
- Combine like terms:
- 2x + 3x - 10 + 40 = 180
- 5x + 30 = 180
Solve for x
- Next, isolate x:
- Subtract 30 from both sides:
- 5x = 180 - 30
- 5x = 150
- Divide by 5:
- x = 150 / 5
- x = 30
Conclusion
- The value of x is 30.
- To verify, substitute x back into the angle measures:
- First angle: 2(30) - 10 = 60 - 10 = 50
- Second angle: 3(30) + 40 = 90 + 40 = 130
- Check the sum:
- 50 + 130 = 180 degrees, confirming that the calculation is correct.
This detailed approach shows how to solve for x in the context of a parallelogram, illustrating the properties of angles within it.
In a parallelogram, adjacent angles are supplementary, meaning they add up to 180 degrees. Given the measures of two adjacent angles as 2x - 10 and 3x + 40, we can set up an equation to find the value of x.
Setting Up the Equation
- The sum of the angles:
- (2x - 10) + (3x + 40) = 180
- Simplifying this:
- Combine like terms:
- 2x + 3x - 10 + 40 = 180
- 5x + 30 = 180
Solve for x
- Next, isolate x:
- Subtract 30 from both sides:
- 5x = 180 - 30
- 5x = 150
- Divide by 5:
- x = 150 / 5
- x = 30
Conclusion
- The value of x is 30.
- To verify, substitute x back into the angle measures:
- First angle: 2(30) - 10 = 60 - 10 = 50
- Second angle: 3(30) + 40 = 90 + 40 = 130
- Check the sum:
- 50 + 130 = 180 degrees, confirming that the calculation is correct.
This detailed approach shows how to solve for x in the context of a parallelogram, illustrating the properties of angles within it.
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What is the value of x if the measure of two adjacent angles of a parallelogram are 2x - 10 and 3x + 40?
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What is the value of x if the measure of two adjacent angles of a parallelogram are 2x - 10 and 3x + 40? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about What is the value of x if the measure of two adjacent angles of a parallelogram are 2x - 10 and 3x + 40? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the value of x if the measure of two adjacent angles of a parallelogram are 2x - 10 and 3x + 40?.
What is the value of x if the measure of two adjacent angles of a parallelogram are 2x - 10 and 3x + 40? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about What is the value of x if the measure of two adjacent angles of a parallelogram are 2x - 10 and 3x + 40? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the value of x if the measure of two adjacent angles of a parallelogram are 2x - 10 and 3x + 40?.
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