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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, we can set up an equation by using the fact that the sum of the angles in a triangle is always 180 degrees:
2x + 3x + 10 + 4x - 19 = 180.
Combining like terms, we get:
9x - 9 = 180.
Adding 9 to both sides of the equation:
9x = 189.
Dividing both sides by 9:
x = 21.
Now that we have the value of x, we can substitute it back into the given expressions to find the measures of all three angles:
- The first angle is 2x: 2(21) = 42 degrees.
- The second angle is 3x + 10: 3(21) + 10 = 73 degrees.
- The third angle is 4x - 19: 4(21) - 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.