Two angles of a triangle are in the ratio 2:4. If the sum of these angles is equal to the sum of the third angle, find the angles of the triangle.
Answers
Answer :
- 30⁰ , 60⁰ , 90⁰ are the angles of the triangle
Given :
- Two angles of a triangle are in the ratio 2 : 4 . If the sum of these angles is equal to the sum of the third angle
To find :
- Angles of the triangle
Solution :
Given
Two angles of a triangle are in the ratio 2:4 so,
- Let the first angle be 2x
- Let the second angle be 4x
And also Given that,
The sum of these angles is equal to the sum of the third angle so
- 2x + 4x = 6x
As we know that
- Sum of all the angles of a triangle is 180⁰
⇢ 2x + 4x + 6x = 180⁰
⇢ 12x = 180⁰
⇢ x = 180/12
⇢ x = 15
Finding the angles of the triangle :
⇢ 2x
⇢ 2(15)
⇢ 30
⇢ 4x
⇢ 4(15)
⇢ 60
⇢ 6x
⇢ 6(15)
⇢ 90
Hence, 30⁰ , 60⁰ , 90⁰ are the angles of the triangle
Verification :
⇢ 2x + 4x + 6x = 180⁰
⇢ 2(15) + 4(15) + 6(15) = 180⁰
⇢ 30 + 60 + 90 = 180⁰
⇢ 180⁰ = 180⁰
Hence , Verified
Step-by-step explanation:
Answer :
30⁰ , 60⁰ , 90⁰ are the angles of the triangle
Given :
Two angles of a triangle are in the ratio 2 : 4 . If the sum of these angles is equal to the sum of the third angle
To find :
Angles of the triangle
Solution :
Given
Two angles of a triangle are in the ratio 2:4 so,
Let the first angle be 2x
Let the second angle be 4x
And also Given that,
The sum of these angles is equal to the sum of the third angle so
2x + 4x = 6x
As we know that
Sum of all the angles of a triangle is 180⁰
⇢ 2x + 4x + 6x = 180⁰
⇢ 12x = 180⁰
⇢ x = 180/12
⇢ x = 15
Finding the angles of the triangle :
⇢ 2x
⇢ 2(15)
⇢ 30
⇢ 4x
⇢ 4(15)
⇢ 60
⇢ 6x
⇢ 6(15)
⇢ 90
Hence, 30⁰ , 60⁰ , 90⁰ are the angles of the triangle
Verification :
⇢ 2x + 4x + 6x = 180⁰
⇢ 2(15) + 4(15) + 6(15) = 180⁰
⇢ 30 + 60 + 90 = 180⁰
⇢ 180⁰ = 180⁰