What is the measure of angle X in the Triangle XYZ if the measure of angle X = x + 20, measure of angle Y = x + 30, and measure of angle Z = x + 40?
To find the measure of angle X in Triangle XYZ, we need to use the information provided about the measures of angles X, Y, and Z.
Given that the measure of angle X is x + 20, the measure of angle Y is x + 30, and the measure of angle Z is x + 40, we can set up an equation to find the value of x.
The sum of the angles in any triangle is always 180 degrees. So, we can write the equation:
(x + 20) + (x + 30) + (x + 40) = 180
Now, let's solve this equation to find the value of x:
Combining like terms, we get:
3x + 90 = 180
Subtracting 90 from both sides of the equation:
3x = 90
Dividing both sides by 3:
x = 30
Now that we know the value of x, we can substitute it back into the expression for angle X to find its measure:
Angle X = x + 20 = 30 + 20 = 50 degrees
Therefore, the measure of angle X in Triangle XYZ is 50 degrees.