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What will be the measure of an angle which is four times its compliment is 10 degree less than twice its compliment.?
Verified Answer
What will be the measure of an angle which is four times its complimen...
First of all we will solve this,
4(90 - a) = 2(180 - a) - 10
360 - 4a = 360 - 2a - 10
2a = 10
a = 5�
The answer for this question is 5�
This question is part of UPSC exam. View all Class 9 courses
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What will be the measure of an angle which is four times its complimen...
Problem:
What will be the measure of an angle which is four times its complement and is 10 degrees less than twice its complement?
Solution:
Let's assume the measure of the angle to be x degrees.
Understanding the problem:
To solve this problem, we need to understand the concepts of angles and their complements.
- An angle and its complement together make a right angle, which is 90 degrees.
- The complement of an angle is the difference between the angle and 90 degrees.
- Two angles are said to be complements if their sum is 90 degrees.
Given information:
- The angle is four times its complement.
- The angle is 10 degrees less than twice its complement.
Formulating equations:
Let's use the given information to set up equations and solve for the angle.
1. The angle is four times its complement:
x = 4(90 - x)
2. The angle is 10 degrees less than twice its complement:
x = 2(90 - x) - 10
Solving the equations:
We can now solve the equations simultaneously to find the value of x.
1. x = 4(90 - x)
x = 360 - 4x
5x = 360
x = 72
2. x = 2(90 - x) - 10
x = 180 - 2x - 10
3x = 170
x ≈ 56.67
Final answer:
The measure of the angle is approximately 56.67 degrees.
What will be the measure of an angle which is four times its complement and is 10 degrees less than twice its complement?
Solution:
Let's assume the measure of the angle to be x degrees.
Understanding the problem:
To solve this problem, we need to understand the concepts of angles and their complements.
- An angle and its complement together make a right angle, which is 90 degrees.
- The complement of an angle is the difference between the angle and 90 degrees.
- Two angles are said to be complements if their sum is 90 degrees.
Given information:
- The angle is four times its complement.
- The angle is 10 degrees less than twice its complement.
Formulating equations:
Let's use the given information to set up equations and solve for the angle.
1. The angle is four times its complement:
x = 4(90 - x)
2. The angle is 10 degrees less than twice its complement:
x = 2(90 - x) - 10
Solving the equations:
We can now solve the equations simultaneously to find the value of x.
1. x = 4(90 - x)
x = 360 - 4x
5x = 360
x = 72
2. x = 2(90 - x) - 10
x = 180 - 2x - 10
3x = 170
x ≈ 56.67
Final answer:
The measure of the angle is approximately 56.67 degrees.
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What will be the measure of an angle which is four times its compliment is 10 degree less than twice its compliment.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about What will be the measure of an angle which is four times its compliment is 10 degree less than twice its compliment.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the measure of an angle which is four times its compliment is 10 degree less than twice its compliment.?.
What will be the measure of an angle which is four times its compliment is 10 degree less than twice its compliment.? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about What will be the measure of an angle which is four times its compliment is 10 degree less than twice its compliment.? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the measure of an angle which is four times its compliment is 10 degree less than twice its compliment.?.
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