# Video: Finding the Size of an Angle Using the Parallel Lines Relation given Its Supplementary Angleβs Size

Find πβ πΆπ΄πΈ.

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### Video Transcript

Find the measure of angle πΆπ΄πΈ.

If we let angle πΆπ΄πΈ equal π₯ and the crossover point in the middle of the diagram be point πΉ, we can solve this problem using our angle properties.

Firstly, we can see that angle π΄πΉπ΅ is equal to 95 degrees as opposite angles are equal. Next, we can see that angle πΉπ΅π΄ is equal to 44 degrees as alternate angles or π angles are also equal.

Angles in a triangle have a sum of 180 degrees. This means that angle πΉπ΄π΅ would be 41 degrees. 95 plus 44 is 139, and 180 minus 139 is 41. Angles on a straight line also add up to 180 degrees. This means that angles πΆπ΄πΈ and angle πΉπ΄π΅ add up to 180.

As angle πΉπ΄π΅ is equal 41 degrees, we can say that π₯ plus 41 equals 180. Subtracting 41 from both sides of this equation gives us a value of π₯ of 139 degrees. This means that angle πΆπ΄πΈ is equal to 139 degrees.