Solve for x. Find the angle measures to check your work.
m<AOB = 4x - 2
m<BOC = 5x + 10
m<COD = 2x + 14
How do I solve for x?
How are points A,B,C,D laid out? Do the angles add up to a right angle, a straight line, a complete circle, or what?
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To solve for x in this problem, we can use the fact that the sum of the angle measures in a straight line is 180 degrees.
1. Write an equation using the sum of the angles in a straight line:
(4x - 2) + (5x + 10) + (2x + 14) = 180
2. Simplify the equation by combining like terms:
4x - 2 + 5x + 10 + 2x + 14 = 180
11x + 22 = 180
3. Subtract 22 from both sides of the equation:
11x = 158
4. Finally, divide both sides of the equation by 11 to solve for x:
x = 158 / 11 = 14.3636 (rounded to four decimal places)
To check your work, substitute this value of x back into each angle measure and verify that the sum of the angles in a straight line equals 180 degrees.
To solve for x, you'll need to set up an equation based on the given angle measures and then solve for x using algebra.
Step 1: Start by summing up all the angle measures around point O. We know that the sum of angles around a point is always 360 degrees. So, we can set up the equation:
m<AOB + m<BOC + m<COD = 360
Substitute the given angle measures:
(4x - 2) + (5x + 10) + (2x + 14) = 360
Step 2: Simplify the equation by combining like terms:
4x + 5x + 2x - 2 + 10 + 14 = 360
11x + 22 = 360
Step 3: Solve for x by isolating the variable on one side of the equation. In this case, subtract 22 from both sides:
11x + 22 - 22 = 360 - 22
11x = 338
Step 4: Divide both sides of the equation by 11 to solve for x:
11x/11 = 338/11
x = 30.73 (rounded to two decimal places)
Now that you have the value of x, you can substitute it back into the original angle measures to find the angle measures:
m<AOB = 4x - 2 = 4(30.73) - 2 = 122.92 degrees
m<BOC = 5x + 10 = 5(30.73) + 10 = 171.64 degrees
m<COD = 2x + 14 = 2(30.73) + 14 = 76.46 degrees
To check your work, you can add up the angle measures:
122.92 + 171.64 + 76.46 = 371.02
Since 371.02 is not equal to 360 (the sum of angles around a point), it's likely that an error was made during the calculations. Double-check your steps to ensure accuracy.