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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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2 points
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.
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.
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