Find the measures of the angles in ∆ABC if m∠A : m∠B:m∠C=2:3:4.
To find the measures of the angles in triangle ∆ABC, we first need to understand how to divide the angles in the ratio of 2:3:4.
Let's suppose the measure of angle A is 2x, the measure of angle B is 3x, and the measure of angle C is 4x.
Since the sum of the angles in a triangle is always 180 degrees, we can write an equation:
2x + 3x + 4x = 180
Now, combine the like terms:
9x = 180
Next, divide both sides of the equation by 9 to solve for x:
x = 180/9
x = 20
Now that we have the value of x, we can find the measures of each angle:
Angle A: 2x = 2(20) = 40 degrees
Angle B: 3x = 3(20) = 60 degrees
Angle C: 4x = 4(20) = 80 degrees
Therefore, the measures of the angles in triangle ∆ABC are: ∠A = 40 degrees, ∠B = 60 degrees, ∠C = 80 degrees.
the sum of the angles of a triangle is 180º
2 n + 3 n + 4 n = 180º
9 n = 180º ... n = 20º
40º + 60º + 80º = 180º