WEBVTT
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Given that π΄π· is a tangent to the circle, find the measure of angle π΅π΄π·.
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The inscribed angle πΆπ΄π΅ is half the measure of the arc.
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This means that angle πΆπ΄π΅ is equal to 94 divided by two.
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94 divided by two is equal to 47 degrees.
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The sum of the angles in a triangle equals 180 degrees.
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Therefore, angle π΄πΆπ΅ is equal to 180 minus 68 plus 47.
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This is equal to 65.
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Therefore, angle π΄πΆπ΅ is equal to 65 degrees.
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The alternate segment theorem states that the angle at the tangent is equal to the opposite interior angle.
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In this case, angle π΅π΄π· or π³ is equal to angle π΄πΆπ΅.
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As angle π΄πΆπ΅ is equal to 65 degrees, then angle π΅π΄π· must also be equal to 65 degrees.
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As π΄π· is a tangent to the circle, the angle π΅π΄π· is 65 degrees.