in a triangle XYZ,the measure of angle Y is 40 more than the measure of angle X.the measure of angle Z is 10 less than three times the measure of angle X.find the measure of angle X

Y = X+40

Z = 3X-10

X+Y+Z = 180
X + X+40 + 3X-10 = 180
5X = 150
X = 30

Let's assume the measure of angle X is represented by "x".

Given:

Angle Y = Angle X + 40

Angle Z = 3 * Angle X - 10

Since the sum of the angles in a triangle is always 180 degrees, we can write the equation:

Angle X + Angle Y + Angle Z = 180

Substituting the given information into the equation, we have:

x + (x + 40) + (3x - 10) = 180

Now, let's solve the equation for x:

Combine like terms:

5x + 30 = 180

Subtract 30 from both sides:

5x = 150

Divide by 5:

x = 30

Therefore, the measure of angle X is 30 degrees.

To find the measure of angle X, we'll set up two equations based on the given information.

Let's say the measure of angle X is "x" degrees.

1. The measure of angle Y is 40 more than the measure of angle X.
So, the measure of angle Y can be expressed as: x + 40 degrees.

2. The measure of angle Z is 10 less than three times the measure of angle X.
So, the measure of angle Z can be expressed as: 3x - 10 degrees.

According to the properties of a triangle, the sum of the interior angles is always 180 degrees. Therefore, we can set up the equation:

x + x + 40 + 3x - 10 = 180

Combining like terms:
5x + 30 = 180

Subtracting 30 from both sides:
5x = 150

Dividing both sides by 5:
x = 30

Hence, the measure of angle X in triangle XYZ is 30 degrees.