### Video Transcript

Is π΄π΅πΆπ· a cyclic
quadrilateral?

We know that the opposite angles in
a cyclic quadrilateral sum to 180 degrees. In this question, we will consider
the opposite angles π΅ and π·. It follows that if these two angles
sum to 180 degrees, then angles π΄ and πΆ must also sum to 180 degrees, as the four
angles inside a quadrilateral sum to 360 degrees.

We can begin this question by
recalling that the three angles inside any triangle sum to 180 degrees. This means that angle π΅ plus 48
degrees plus 29 degrees must equal 180 degrees. 48 plus 29 is equal to 77. Subtracting 77 degrees from both
sides of this equation gives us angle π΅ is equal to 103 degrees. We can now go back to our statement
about a cyclic quadrilateral. We know that angle π΅ is equal to
103 degrees and angle π· is equal to 77 degrees. These two indeed sum to 180
degrees.

As previously mentioned, if angle
π΅ plus angle π· sum to 180 degrees, then angle π΄ plus angle πΆ must also sum to
180 degrees. This is because the four angles
inside the quadrilateral π΄π΅πΆπ· must sum to 360 degrees. We can therefore conclude that yes,
π΄π΅πΆπ· is a cyclic quadrilateral.