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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, you need to solve the equation involving the three angles of the triangle.
The sum of the angles in a triangle is always 180 degrees. So, you need to set up an equation:
2x + (3x + 10) + (4x - 19) = 180
Simplifying 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
To find the measures of the three angles, substitute the value of x back into the expressions given:
First angle: 2x = 2 * 21 = 42 degrees
Second angle: 3x + 10 = 3 * 21 + 10 = 73 degrees
Third angle: 4x - 19 = 4 * 21 - 19 = 85 degrees
So the value of x is 21, and the measures of the three angles are 42 degrees, 73 degrees, and 85 degrees.