if angles of a triangle are in the ratio 2:3:4.Find the value of each angle
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If the angles of a triangle are in the ratio of... 2 :3 :4 then we can divide the Total Degrees of the Triangle i.e 180 degrees in that order as below : 2+3+4 = 9 Parts of 180 is … 180/9 = 20 degrees.
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Given, <A : <B : <C is equal to 2:3:4, let’s assume the values of angles as,
<A = 2x
<B = 3x
<C = 4x,
x is a whole number. You can see that we have taken the values of angles such that they are still in the ratio 2:3:4.
Now, we know that the sum of all the angles of a triangle is 180°.
So, in triangle ABC
<A + <B + <C = 180°
Putting values of angles,
2x + 3x + 4x = 180°
9x = 180°
x = 180°/9
x = 20°
So, angles are as follows,
<A = 2(x) = 2(20°) = 40°
<B = 3(x) = 3(20°) = 60°
<C = 4(x) = 4(20°) = 80°
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