Question Video: Proving a Geometric Property Using Vertical Opposition of Angles | Nagwa Question Video: Proving a Geometric Property Using Vertical Opposition of Angles | Nagwa

# Question Video: Proving a Geometric Property Using Vertical Opposition of Angles Mathematics • First Year of Preparatory School

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In the given figure, find the measure of β ππΆπ.

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### Video Transcript

In the given figure, find the measure of angle ππΆπ.

Observe that angle πΆπ΄π΅ is vertically opposite angle ππ΄πΏ. This means that the two angles are congruent. Similarly, angle π΄π΅πΆ is vertically opposite and, therefore, congruent to angle ππ΅π. Since π΄π΅πΆ is a triangle, we know that its internal angles sum to 180 degrees.

The internal angles of triangle π΄π΅πΆ are angles πΆπ΄π΅, π΄π΅πΆ, and π΅πΆπ΄. Therefore, angle π΅πΆπ΄ has measure 180 minus 80 minus 30 equals 70 degrees. Finally, since angle ππΆπ is vertically opposite angle π΅πΆπ΄, the two angles are congruent. Therefore, angle ππΆπ has measure 70 degrees.

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