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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.

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To find the value of x and the measures of all three angles, we need to use the fact that the sum of all angles in a triangle is always 180 degrees.

Let's set up an equation based on this information:

2x + 3x + 10 + 4x - 19 = 180

Combine like terms:

9x - 9 = 180

Add 9 to both sides:

9x = 189

Divide both sides by 9:

x = 21

Now that we have found the value of x, we can substitute it into the expressions for each angle to find their measures:

First angle: 2x = 2(21) = 42 degrees
Second angle: 3x + 10 = 3(21) + 10 = 63 + 10 = 73 degrees
Third angle: 4x - 19 = 4(21) - 19 = 84 - 19 = 65 degrees

Therefore, the value of x is 21, and the measures of the three angles are 42 degrees, 73 degrees, and 65 degrees.
shorter
To find the value of x, we need to solve the equation:

2x + 3x + 10 + 4x - 19 = 180

Combine like terms:

9x - 9 = 180

Add 9 to both sides:

9x = 189

Divide both sides by 9:

x = 21

Now that we have x, we can substitute it into each expression for the angles to find their measures:

First angle: 2x = 2(21) = 42 degrees
Second angle: 3x + 10 = 3(21) + 10 = 73 degrees
Third angle: 4x - 19 = 4(21) - 19 = 65 degrees

Therefore, x = 21 and the measures of the three angles are 42 degrees, 73 degrees, and 65 degrees.
just replace therefore with so
and we with I
To find the value of x, I need to solve the equation:

2x + 3x + 10 + 4x - 19 = 180

Combining like terms:

9x - 9 = 180

Adding 9 to both sides:

9x = 189

Dividing both sides by 9:

x = 21

Now that I have x, I can substitute it into each expression for the angles to find their measures:

First angle: 2x = 2(21) = 42 degrees
Second angle: 3x + 10 = 3(21) + 10 = 73 degrees
Third angle: 4x - 19 = 4(21) - 19 = 65 degrees

So, x = 21 and the measures of the three angles are 42 degrees, 73 degrees, and 65 degrees.
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