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.