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.
what is x
To find the value of x, we need to use the fact that the sum of the angles in a triangle is always 180 degrees.
So, we can set up the equation:
2x + 3x + 10 + 4x - 19 = 180
Combining like terms, we get:
9x - 9 = 180
Adding 9 to both sides:
9x = 189
Dividing both sides by 9:
x = 21
Therefore, x is equal to 21.
To find the measures of all three angles, we can substitute x = 21 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 measures of all three angles are: 42 degrees, 73 degrees, and 85 degrees.