The measures of the angles of a triangle are in the ratio 1:2:3. Find half the measure of the largest angle?
let the angles be x, 2x, and 3x
x+2x+3x=180
x=30
So the largest is 3(30) = 90
and half of that is 45 degrees.
To find the measure of each angle in a triangle when given the ratio, you need to start by assigning a variable to represent the ratio. Let's call the ratio "x."
In this case, the ratio is given as 1:2:3. This means that the three angles can be represented as x, 2x, and 3x, respectively.
The sum of the angles in a triangle is always 180 degrees. Therefore, you can write an equation to solve for x:
x + 2x + 3x = 180
Combine like terms:
6x = 180
Divide both sides by 6:
x = 30
Now that you have found the value of x, substitute it back into the given ratio to find the measure of each angle:
1st angle: x = 30 degrees
2nd angle: 2x = 2 * 30 = 60 degrees
3rd (largest) angle: 3x = 3 * 30 = 90 degrees
To find half the measure of the largest angle (90 degrees), simply divide it by 2:
Half the measure of the largest angle = 90 degrees / 2 = 45 degrees
Therefore, half the measure of the largest angle in the triangle is 45 degrees.