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Find the angle x and give full reasons for your answer

Find The Angle X And Give Full Reasons For Your Answer class=

Sagot :

reinhard10158

Answer:

x = 120°

Step-by-step explanation:

alternate segment theorem :

the angle between a tangent c (like here TB) and a chord (like here TC) is equal to the angle subtended (top angle in a triangle) by the same cord in the alternate (opposite or complementary) segment (like here D in the segment/triangle TCD).

so, the chord TC cuts the circle into 2 segments : the large TC arc, and the smaller TCD arc.

and the angle of the tangent at T with the chord TC (120°) is the same as the angle at the top of the triangle inscribed into the TCD segment (the alternate segment to the large TC segment).

FYI

you can play around with it : e.g. if you move C so that we have a right angle (90°) at T, the chord TC turns into a diameter of the circle, and the angle at D has also to be 90° (an additional theorem "angles in a semi-circle"). and so on.

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