The measures of the angles in a triangle are in the extended ratio 3:4:5. Find the measures of the angles.
show work
x =
m∠1 = °
m∠2 = °
m∠3 = °
The angles are 3x,4x,5x
Sum them up and you have 12x=180
Now find x, and thus the angles.
Angle 1 = 45
Angle 2 = 60
Angle 3 = 75
x = 15
I followed Steve's approach and that's what I got. I divided 12 by 180 and got 15 then multiplied 3, 4, and 5. That's how I got 45, 60, and 75.
To find the measures of the angles in a triangle, we can use the extended ratio given.
Let's assume that the measures of the angles are 3x, 4x, and 5x.
According to the extended ratio, the measures of the angles are in a ratio of 3:4:5.
Therefore, we have:
Angle 1 = 3x
Angle 2 = 4x
Angle 3 = 5x
To find the value of x, we can use the fact that the sum of the angles in a triangle is 180 degrees.
Sum of the angles in a triangle = Angle 1 + Angle 2 + Angle 3
180 = 3x + 4x + 5x
Simplifying the equation, we get:
180 = 12x
Now, we can solve for x by dividing both sides of the equation by 12:
x = 180/12
x = 15
Now that we have the value of x, we can substitute it back into the expressions for the angles to find their measures.
Angle 1 = 3x = 3 * 15 = 45 degrees
Angle 2 = 4x = 4 * 15 = 60 degrees
Angle 3 = 5x = 5 * 15 = 75 degrees
Therefore, the measures of the angles are:
Angle 1 = 45 degrees
Angle 2 = 60 degrees
Angle 3 = 75 degrees