The values of x, y and z in the figure are 123, 171 and -114 respectively
Alternating Angle Theorem
Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. Alternate angles are equal: We can often spot interior alternate angles by drawing a Z shape: There are two different types of alternate angles, alternate interior angles and alternate exterior angles.
Using this theorem, we can simply say that;
4z + 3y = y + z
However, we can apply corresponding angles theorem too;
57 = y + z
We can say that
4z + 3y = 57
However, angles on a straight line is equal to 180 degrees
x + (y+ z) = 180
x + 57 = 180
x = 123
Now, we can set up a set of system of equations to solve for y and z
4z + 3y = 57 ... equation (i)
y + z = 57 ... equation (ii)
y = 171, z = -114
Learn more on alternating angles here;
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