Find the relationships between the angles and use corresponding theorems and postulates.
x=40 by the Corresponding Angles Postulate
y=50 by the Supplement 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 3x-15 and 105 are corresponding angles.
Let's recall that, by the Corresponding Angles Postulate, the corresponding angles formed by parallel lines and a transversal are congruent. Therefore, these angles are congruent and their measures are the same.
3x-15= 105
Let's solve this equation for x.
The value of x is 40 by the Corresponding Angles Theorem.
Value of y
Next, observing the diagram, we can see that the angles that measure y+25 and 3x-15 are supplementary angles.
Recall that, by the Supplement Theorem, the sum of the measures of the supplementary angles is 180.
( 3x-15)+( y+25)=180
⇕
3x+y+10=180
Since we already know that x=40, we can substitute this value into the equation, and solve for y.
