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.

Question

You need to solve for x then substitute the value for x in the expressions to find the angle measure. 

Answer 1

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.

Answer 2

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?

Answer 3

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.