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Find πβ πΆ.

Find the measure of angle πΆ.

We can see from the diagram that the line π΄π΅ is parallel to the line πΆπ·. In this question, we need to calculate the measure of angle πΆ. We begin by looking at the point π΄, noting that angles at a point or in a circle sum to 360 degrees. If we let the missing angle be π₯, then π₯ plus 123 plus 132 is equal to 360. Simplifying this gives us π₯ plus 255 is equal to 360. Subtracting 255 from both sides of this equation gives us π₯ is equal to 105. The missing angle at point π΄ is 105 degrees.

As mentioned previously, lines π΄π΅ and πΆπ· are parallel. The line π΄πΆ creates two cointerior or supplementary angles. As these sum to 180 degrees, the angle π¦ at point πΆ plus 105 must equal 180. Subtracting 105 from both sides of this equation gives us π¦ is equal to 75. We can therefore conclude that the measure of angle πΆ is equal to 75 degrees.

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