the measures of three angles of a triangle are in the ratio 4:5:6. Find the measure of each
Ah, the ancient riddle of the triangle angles! Well, if we assign the ratio as 4x:5x:6x, we can solve this math mystery. Let's add up the angles, shall we?
4x + 5x + 6x = 180 degrees, because the sum of all angles in a triangle is always 180 degrees.
Now, let's simplify this equation.
15x = 180 degrees
Divide both sides by 15:
x = 12 degrees
Now, we can find the measure of each angle by substituting x back into the ratio:
Angle 1: 4x = 4 * 12 = 48 degrees
Angle 2: 5x = 5 * 12 = 60 degrees
Angle 3: 6x = 6 * 12 = 72 degrees
So, the measure of each angle in this triangle is 48 degrees, 60 degrees, and 72 degrees. Voilà!
To find the measure of each angle in a triangle given the ratio of their measures, you need to compute the value of each part of the ratio, then multiply it by the corresponding constant factor.
Let's assume the measures of the angles are 4x, 5x, and 6x, where x is the constant factor.
Since the sum of the three angles in a triangle is always 180 degrees, we can set up an equation:
4x + 5x + 6x = 180
Combining like terms, we get:
15x = 180
To solve for x, divide both sides of the equation by 15:
x = 180/15 = 12
Now that we have the value of x, we can find the measure of each angle:
Angle 1: 4x = 4 * 12 = 48 degrees
Angle 2: 5x = 5 * 12 = 60 degrees
Angle 3: 6x = 6 * 12 = 72 degrees
Therefore, the measures of the three angles are 48 degrees, 60 degrees, and 72 degrees.
To find the measure of each angle of the triangle, we need to follow these steps:
Step 1: Determine the sum of the measures of the three angles of a triangle. In any triangle, the sum of the angles is always 180 degrees.
Step 2: Write the ratio of the measures of the angles. In this case, the given ratio is 4:5:6.
Step 3: Assign variables to the measures of the angles. Let's call them 4x, 5x, and 6x.
Step 4: Set up an equation using the given ratio. Since the sum of the angles is 180 degrees, we can write the equation as follows:
4x + 5x + 6x = 180
Step 5: Simplify and solve the equation:
15x = 180
Divide both sides by 15:
x = 12
Step 6: Substitute the value of x back into the expressions for the angles to find their measures:
Angle 1: 4x = 4 * 12 = 48 degrees
Angle 2: 5x = 5 * 12 = 60 degrees
Angle 3: 6x = 6 * 12 = 72 degrees
Therefore, the measures of the three angles of the triangle are 48 degrees, 60 degrees, and 72 degrees.
Sum of ratios is:
4+5+6=15
A=(4/15)*180°=(4*180°/15)=(720°/15)=48°
B=(5/15)*180°=(180°/3)=60°
Becouse (5/15)=(1/3)
C=(6/15)*180°=(6*180°/15)=(1080°/15)=72°
A= 48° , B= 60° , C=72°
A+B+C=48°+60°+72°=180°