When two parallel tangents drawn of a circle to meet a third tangent, how do you prove that the sum of interior angles of a transversal is equal to 180?
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Proof :
Given, Two parallel tangents drawn of a circle to meet a third Tangent.
Join the point of contact of the Tangent with the circle to the centre ( For both parallel tangents)
Since, the tangents are parallel, The line will be continuous. As you can observe in the picture, It forms a four sided polygon ( Say Quadrilateral).
We know that, Sum of all interior angles in a four sided polygon will be 360°. ~ ( 1)
Also, Tangent is perpendicular to Radius. Hence,
Therefore, Angle A = 90
Angle B = 90
From (1)
A + B + C + D = 360
90 + 90 + C + D = 360
C + D = 180.
Hence, When two parallel tangents drawn of a circle to meet a third tangent, the sum of interior angles of a transversal is equal to 180.
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Anonymous:
Thanks :))
Sup..Sup... Superb Answer Sir :-)
From the converse of above we can say that if the two lines are parallel then the sum of interior angle of transversal are supplementary i.e. their sum is 180°Angle Alpha + Angle Beta =180°Hence proved.}
{The same proof can be given in many ways this is one of themWe can also proved it by making a tangent at a point which makes an angle of 90° }
{With the parallel so from that we simply says that sum of interior angles }
HOPE IT HELPS:----
Please mark as verified answer:----
{The same proof can be given in many ways this is one of themWe can also proved it by making a tangent at a point which makes an angle of 90° }
{With the parallel so from that we simply says that sum of interior angles }
HOPE IT HELPS:----
Please mark as verified answer:----
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