A triangular playground has angles with measures in the ration 8:4:6. What is the measure of the smallest angle?
The ratio of the measures of the angles can be expressed as 8x:4x:6x, where x is a positive number.
The sum of the measures of the angles in a triangle is 180 degrees.
So, 8x + 4x + 6x = 180.
Combining like terms, we have 18x = 180.
Dividing both sides by 18, we get x = 10.
Therefore, the measures of the angles are 8x = 80 degrees, 4x = 40 degrees, and 6x = 60 degrees.
The smallest angle is 40 degrees.
To find the measure of the smallest angle in the triangular playground, we first need to determine the angle measures using the given ratio.
Let's assume that the three angles of the triangle have measures 8x, 4x, and 6x, where x is a constant.
To find the value of x, we know that the sum of the measures of the angles in a triangle is always 180 degrees.
So, we can write the equation:
8x + 4x + 6x = 180.
Combining like terms:
18x = 180.
Dividing both sides of the equation by 18 gives us:
x = 180 / 18 = 10.
Now that we know the value of x, we can substitute it back into the angle measures:
8x = 8 * 10 = 80 degrees.
4x = 4 * 10 = 40 degrees.
6x = 6 * 10 = 60 degrees.
Therefore, the measure of the smallest angle is 40 degrees.
To find the measure of the smallest angle, we first need to find the sum of the angle measures in the triangular playground.
The ratio of the angle measures is 8:4:6, which means that we can assign variables to represent the measures. Let's call the measures 8x, 4x, and 6x, respectively.
The sum of all the angles in a triangle is always 180 degrees. So, we can write the following equation:
8x + 4x + 6x = 180
Combine like terms:
18x = 180
Solve for x by dividing both sides of the equation by 18:
18x/18 = 180/18
x = 10
Now that we know the value of x, we can substitute it back into our expressions for the angle measures:
Smallest angle = 4x = 4(10) = 40 degrees
Therefore, the measure of the smallest angle in the triangular playground is 40 degrees.