The value of ∠B is 60 degrees
How to solve for B?
The given parameters are
2∠A = 3∠B = 6∠C
Let the angles in a triangle ABC be ∠A, ∠B and ∠C.
The sum of these angles in the triangle ABC is
∠A + ∠B + ∠C = 180
Multiply the above equation by 2
2 * (∠A + ∠B + ∠C) = 2 * 180
Evaluate the product
2∠A + 2∠B + 2∠C = 360
Recall that 2∠A = 3∠B.
Substitute the above in the equation 2∠A + 2∠B + 2∠C = 360
3∠B + 2∠B + 2∠C = 360
This gives
5∠B + 2∠C = 360
Multiply the above equation by 3
3 * (5∠B + 2∠C) = 3 * 360
Evaluate the product
15∠B + 6∠C = 1080
Recall that 3∠B = 6∠C.
Substitute the above in the equation
So, we have:
15∠B + 3∠B = 1080
Evaluate the like terms
18∠B = 1080
Divide both sides by 18
∠B = 60
Hence, the value of ∠B is 60 degrees
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