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The angle A of a triangle ABC is equal to the sum of the other two angles also the ratio of the angle B to the angle C is 2 : 3 , then 3 angles are?
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The angle A of a triangle ABC is equal to the sum of the other two ang...
Given information:
- Angle A = Angle B + Angle C
- Angle B : Angle C = 2 : 3
Solution:
Step 1: Expressing angles in terms of variables
Let's assume:
Angle B = 2x
Angle C = 3x
Step 2: Using the first given information
According to the first given information:
Angle A = Angle B + Angle C
A = 2x + 3x
A = 5x
Step 3: Sum of angles in a triangle
The sum of angles in a triangle is 180 degrees.
Therefore:
A + B + C = 180
5x + 2x + 3x = 180
10x = 180
x = 18
Step 4: Calculating the angles
Now, substitute the value of x back into the expressions for angles B and C:
Angle B = 2x = 2 * 18 = 36 degrees
Angle C = 3x = 3 * 18 = 54 degrees
Angle A = 5x = 5 * 18 = 90 degrees
Conclusion:
The three angles of the triangle ABC are:
Angle A = 90 degrees
Angle B = 36 degrees
Angle C = 54 degrees
- Angle A = Angle B + Angle C
- Angle B : Angle C = 2 : 3
Solution:
Step 1: Expressing angles in terms of variables
Let's assume:
Angle B = 2x
Angle C = 3x
Step 2: Using the first given information
According to the first given information:
Angle A = Angle B + Angle C
A = 2x + 3x
A = 5x
Step 3: Sum of angles in a triangle
The sum of angles in a triangle is 180 degrees.
Therefore:
A + B + C = 180
5x + 2x + 3x = 180
10x = 180
x = 18
Step 4: Calculating the angles
Now, substitute the value of x back into the expressions for angles B and C:
Angle B = 2x = 2 * 18 = 36 degrees
Angle C = 3x = 3 * 18 = 54 degrees
Angle A = 5x = 5 * 18 = 90 degrees
Conclusion:
The three angles of the triangle ABC are:
Angle A = 90 degrees
Angle B = 36 degrees
Angle C = 54 degrees
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The angle A of a triangle ABC is equal to the sum of the other two angles also the ratio of the angle B to the angle C is 2 : 3 , then 3 angles are?
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The angle A of a triangle ABC is equal to the sum of the other two angles also the ratio of the angle B to the angle C is 2 : 3 , then 3 angles are? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The angle A of a triangle ABC is equal to the sum of the other two angles also the ratio of the angle B to the angle C is 2 : 3 , then 3 angles are? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The angle A of a triangle ABC is equal to the sum of the other two angles also the ratio of the angle B to the angle C is 2 : 3 , then 3 angles are?.
The angle A of a triangle ABC is equal to the sum of the other two angles also the ratio of the angle B to the angle C is 2 : 3 , then 3 angles are? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The angle A of a triangle ABC is equal to the sum of the other two angles also the ratio of the angle B to the angle C is 2 : 3 , then 3 angles are? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The angle A of a triangle ABC is equal to the sum of the other two angles also the ratio of the angle B to the angle C is 2 : 3 , then 3 angles are?.
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