m<AOB=4x-2,m<BOC=5x+10,m<COD=2x+14
How do you solve the equation? And how do you find the measurement of each of the 3 given angles??
Well, solving this equation is no joke! Let's break it down step by step.
Step 1: Add up the measures of the angles in a straight line. We know that a straight line forms a 180-degree angle.
So, m<AOB + m<BOC + m<COD = 180
Step 2: Substitute the given values into the equation.
4x - 2 + 5x + 10 + 2x + 14 = 180
Step 3: Combine like terms and simplify.
11x + 22 = 180
Step 4: Solve for x.
11x = 180 - 22
11x = 158
x = 158 / 11
x ≈ 14.36
Step 5: Now, substitute the value of x into each equation to find the measure of each angle.
m<AOB = 4x - 2
m<AOB = (4 * 14.36) - 2
m<AOB ≈ 57.44 degrees
m<BOC = 5x + 10
m<BOC = (5 * 14.36) + 10
m<BOC ≈ 80.8 degrees
m<COD = 2x + 14
m<COD = (2 * 14.36) + 14
m<COD ≈ 42.72 degrees
So, the measurement of angle AOB is approximately 57.44 degrees, the measurement of angle BOC is approximately 80.8 degrees, and the measurement of angle COD is approximately 42.72 degrees.
Hope that solves your equation conundrum with a twist of humor!
To solve the equation and find the measurement of each of the three given angles, we can set up an equation involving the angles.
Step 1: Set up the equation.
According to the information given, the three angles m<AOB, m<BOC, and m<COD are related by the equation:
m<AOB + m<BOC + m<COD = 180 degrees
Step 2: Substitute the given expressions for the angles into the equation.
Substitute the given expressions for the angles:
(4x-2) + (5x+10) + (2x+14) = 180
Step 3: Simplify and solve for x.
Combine like terms on the left side of the equation:
4x - 2 + 5x + 10 + 2x + 14 = 180,
11x + 22 = 180.
Subtract 22 from both sides of the equation:
11x = 158.
Divide both sides by 11 to solve for x:
x = 158/11.
Step 4: Find the measurement of each angle.
Now that we have the value of x, we can substitute it into the expressions to find the measurements of the angles.
m<AOB = 4x - 2 = 4(158/11) - 2,
m<BOC = 5x + 10 = 5(158/11) + 10,
m<COD = 2x + 14 = 2(158/11) + 14.
Simplify each expression to find the measurements of the angles.
To solve the equation and find the measurement of each of the three given angles, we need to apply the properties of angles in a straight line and angles around a point.
1. Angles in a straight line: In a straight line, the sum of the angles is 180 degrees. Therefore, we can set up an equation for the sum of angles AOB, BOC, and COD:
m<AOB + m<BOC + m<COD = 180
2. Substitute the given expressions for the angles:
4x-2 + 5x+10 + 2x+14 = 180
Now, we can solve this equation to find the value of x.
3. Simplify the equation by combining like terms:
11x + 22 = 180
4. Move the constant term to the other side of the equation:
11x = 180 - 22
5. Continue simplifying:
11x = 158
6. Solve for x by dividing both sides of the equation by 11:
x = 158/11
7. Calculate the value of x:
x ≈ 14.36
Now that we have the value of x, we can substitute it back into the given expressions to find the measurement of each angle:
m<AOB = 4x - 2 = 4 * 14.36 - 2 ≈ 55.44 degrees
m<BOC = 5x + 10 = 5 * 14.36 + 10 ≈ 78.8 degrees
m<COD = 2x + 14 = 2 * 14.36 + 14 ≈ 42.72 degrees
Therefore, the measurement of angle AOB is approximately 55.44 degrees, the measurement of angle BOC is approximately 78.8 degrees, and the measurement of angle COD is approximately 42.72 degrees.