Question 3: The measure of one angle in a triangle is 2x degrees, the second angle is 3x + 10 degrees, and the third angle is 4x - 19 degrees. Find the value of x and the measures of all three angles.
You need to solve for x then substitute the value for x in the expressions to find the angle measure.
To solve for x, we know that the sum of the angles in a triangle is always 180 degrees.
So, we can write the equation:
2x + (3x + 10) + (4x - 19) = 180
Simplifying the equation:
2x + 3x + 10 + 4x - 19 = 180
9x - 9 = 180
Adding 9 to both sides:
9x = 189
Dividing both sides by 9:
x = 21
Now that we have found the value of x, we can substitute it back into the expressions for the angles to find their measures.
Angle 1: 2x = 2 * 21 = 42 degrees
Angle 2: 3x + 10 = 3 * 21 + 10 = 73 degrees
Angle 3: 4x - 19 = 4 * 21 - 19 = 65 degrees
So, the value of x is 21 and the measures of the three angles are: 42 degrees, 73 degrees, and 65 degrees.
Step one: Set up the equation 2x + (3x + 10) + (4x - 19) = 180
2x + 3x + 4x = 9x
19 - 10 = 9
9x = 180
x = 19
is this correct?
No, that is not correct. Let's go through the equation again:
2x + (3x + 10) + (4x - 19) = 180
Combining like terms within the parentheses:
2x + 3x + 4x + 10 - 19 = 180
9x - 9 = 180
Adding 9 to both sides:
9x = 189
Dividing both sides by 9:
x = 21
So the correct value of x is 21, not 19.