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If two conplementry angles are such that two times the measure of one is equal to to three times the measure of the other than find the measure of larger angle?
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If two conplementry angles are such that two times the measure of one ...
Here’s a detailed explanation to find the measure of the larger angle among two complementary angles given the condition:
Understanding Complementary Angles
- Complementary angles are two angles that sum up to 90 degrees.
- If we denote the two angles as \( x \) and \( y \), we can write the equation:
\( x + y = 90 \).
Setting Up the Equations
- According to the problem, two times the measure of one angle is equal to three times the measure of the other.
- We can express this relationship mathematically as:
\( 2x = 3y \).
Substituting Values
- From the first equation, we can express \( y \) in terms of \( x \):
\( y = 90 - x \).
- Now, substitute \( y \) into the second equation:
\( 2x = 3(90 - x) \).
Simplifying the Equation
- Distributing the 3 gives:
\( 2x = 270 - 3x \).
- Combining like terms leads to:
\( 2x + 3x = 270 \),
which simplifies to:
\( 5x = 270 \).
Finding the Value of x
- Solving for \( x \):
\( x = \frac{270}{5} = 54 \) degrees.
Calculating the Other Angle
- Substitute \( x \) back into the equation for \( y \):
\( y = 90 - 54 = 36 \) degrees.
Conclusion: Measure of the Larger Angle
- The larger angle is:
\( \text{Larger angle} = 54 \) degrees.
Thus, the measure of the larger angle among the two complementary angles is 54 degrees.
Understanding Complementary Angles
- Complementary angles are two angles that sum up to 90 degrees.
- If we denote the two angles as \( x \) and \( y \), we can write the equation:
\( x + y = 90 \).
Setting Up the Equations
- According to the problem, two times the measure of one angle is equal to three times the measure of the other.
- We can express this relationship mathematically as:
\( 2x = 3y \).
Substituting Values
- From the first equation, we can express \( y \) in terms of \( x \):
\( y = 90 - x \).
- Now, substitute \( y \) into the second equation:
\( 2x = 3(90 - x) \).
Simplifying the Equation
- Distributing the 3 gives:
\( 2x = 270 - 3x \).
- Combining like terms leads to:
\( 2x + 3x = 270 \),
which simplifies to:
\( 5x = 270 \).
Finding the Value of x
- Solving for \( x \):
\( x = \frac{270}{5} = 54 \) degrees.
Calculating the Other Angle
- Substitute \( x \) back into the equation for \( y \):
\( y = 90 - 54 = 36 \) degrees.
Conclusion: Measure of the Larger Angle
- The larger angle is:
\( \text{Larger angle} = 54 \) degrees.
Thus, the measure of the larger angle among the two complementary angles is 54 degrees.
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If two conplementry angles are such that two times the measure of one is equal to to three times the measure of the other than find the measure of larger angle?
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If two conplementry angles are such that two times the measure of one is equal to to three times the measure of the other than find the measure of larger angle? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If two conplementry angles are such that two times the measure of one is equal to to three times the measure of the other than find the measure of larger angle? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If two conplementry angles are such that two times the measure of one is equal to to three times the measure of the other than find the measure of larger angle?.
If two conplementry angles are such that two times the measure of one is equal to to three times the measure of the other than find the measure of larger angle? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If two conplementry angles are such that two times the measure of one is equal to to three times the measure of the other than find the measure of larger angle? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If two conplementry angles are such that two times the measure of one is equal to to three times the measure of the other than find the measure of larger angle?.
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