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If the measure of three angles of a triangle are in the ratio 2 : 3 : 5, then the triangle is: (SSC CGL 1st Sit. 2015)
- a)equilateral
- b)isocsceles
- c)Obtuse angled
- d)right angled
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If the measure of three angles of a triangle are in the ratio 2 : 3 : ...
Sum of the angle of a triangle = 180°
⇒ 2x° + 3x° + 5x° = 180°
⇒ 10x° = 180°
x° = 18°
Angle are = 36°, 54°, 90° So, this is right angles triangle.
⇒ 2x° + 3x° + 5x° = 180°
⇒ 10x° = 180°
x° = 18°
Angle are = 36°, 54°, 90° So, this is right angles triangle.
Most Upvoted Answer
If the measure of three angles of a triangle are in the ratio 2 : 3 : ...
Sum of the angle of a triangle = 180°
⇒ 2x° + 3x° + 5x° = 180°
⇒ 10x° = 180°
x° = 18°
Angle are = 36°, 54°, 90° So, this is right angles triangle.
⇒ 2x° + 3x° + 5x° = 180°
⇒ 10x° = 180°
x° = 18°
Angle are = 36°, 54°, 90° So, this is right angles triangle.
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If the measure of three angles of a triangle are in the ratio 2 : 3 : ...
Explanation:
Given:
- The measure of three angles of a triangle are in the ratio 2 : 3 : 5.
Solution:
Step 1: Find the total sum of angles in a triangle
- Let the three angles be 2x, 3x, and 5x (since they are in the ratio 2 : 3 : 5).
- According to the property of triangles, the sum of all angles in a triangle is 180 degrees.
- Therefore, 2x + 3x + 5x = 180.
- Solving the equation, we get x = 12.
Step 3: Determine the type of triangle based on the angles
- Now we substitute the value of x back into the angles: 2x = 24, 3x = 36, and 5x = 60.
- The angles of the triangle are 24°, 36°, and 60°.
- Since the angles are 24°, 36°, and 60°, they form a right-angled triangle.
- Therefore, the triangle is a right-angled triangle.
Therefore, the correct answer is option 'D' - right-angled triangle.
Given:
- The measure of three angles of a triangle are in the ratio 2 : 3 : 5.
Solution:
Step 1: Find the total sum of angles in a triangle
- Let the three angles be 2x, 3x, and 5x (since they are in the ratio 2 : 3 : 5).
- According to the property of triangles, the sum of all angles in a triangle is 180 degrees.
- Therefore, 2x + 3x + 5x = 180.
- Solving the equation, we get x = 12.
Step 3: Determine the type of triangle based on the angles
- Now we substitute the value of x back into the angles: 2x = 24, 3x = 36, and 5x = 60.
- The angles of the triangle are 24°, 36°, and 60°.
- Since the angles are 24°, 36°, and 60°, they form a right-angled triangle.
- Therefore, the triangle is a right-angled triangle.
Therefore, the correct answer is option 'D' - right-angled triangle.
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