Find the relationships between the angles and use corresponding theorems and postulates.
x=125 by the Supplement Theorem
y=125 by the Alternate Interior Angles Theorem
Practice makes perfect
Consider the diagram below. In order to find the values of the variables, we need to find the relationships between the angles and use the corresponding theorems and postulates.
Let's calculate each value one at a time.
Value of x
Looking at the diagram, we can see that the angles that measure 55 and x are supplementary angles.
Let's recall that, by the Supplement Theorem, the sum of the measures of the supplementary angles is 180.
x+ 55=180
Now let's solve the equation for x.
Now we can see that the angles that measure y and 125 lie on opposite sides of the transversal. Therefore, they are interior angles formed by parallel lines.
If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.
By this theorem, we know that the alternate interior angles are congruent, and their measures are the same.
y= 125
The value of y is 125 by the Alternate Interior Angles Theorem.
