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Using Properties of Parallel Lines

Using Properties of Parallel Lines 1.7 - Solution

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Let's start by finding the value of Then, we will use its value to find

Value of

To find the value of we need to know the relationship between the angles with measures and Let's analyze the given diagram.

These are corresponding angles. The Corresponding Angles Postulate tells us that corresponding angles formed by parallel lines and a transversal are congruent. Therefore, these angles are congruent and their measures are the same. Let's solve this equation!

Value of

Now, we can find the value of

The angles with measures and form a linear pair. This tells us that they are supplementary angles. Therefore, the sum of their measures is Since we already know that we can substitute this value in the above equation, and solve for
Solve for