If ABCD is an isosceles trapezium, then angle C is equal to:

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Depends on the naming of the trapezium

answer is D.

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Detailed Solution

Concept- Here we use the isosceles trapezoid property to see which angle is equal to

. There are two cases, depending on the name of the trapezoid. The first case is when

is adjacent to

and the second case is when

is on the opposite basis to

. It also uses the property that the isosceles trapezoids have the same base angle.
In an isosceles trapezoid, the two opposite sides are parallel and the other two sides are the same length. The diagonals are the same length and the base angles are the same size.
Here in the first case when

and

are adjacent to each other
Question Image

Since we know that the base angles of the isosceles trapezoids are equal, here

In the second case

is on the other base as that of

The base angle of the isosceles trapezoid is the same here, so you can write it as follows.

Hence, the correct answer is option 4) depends on the naming of the trapezium

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