If abcd is an isosceles trapezium what is the measure of angle c

1. Relation Between the Two Sides of a Triangle and Their Opposite Angles:

(i) The opposite angles of the arms of same length are equal to each other.

(ii) The length of opposite sides of two angles equal in measurement of a triangle are equal.

2. Congruency of triangles:

(i) SAS Congruency: Two triangles are congruent if length of two sides and the measurement of included angle of one triangle are equal to the length of two sides and the measurement of included angle of the other triangle.

(ii) AAS Congruency: Two triangles are congruent if measurement of any pair of angles and length of one pair of corresponding sides are equal to the other triangle.

(iii) SSS Congruency: Two triangles are congruent if the length of three sides of one triangle is equal to the length of three sides of another triangle then the two triangles are congruent.

(iv) RHS Congruency: Two triangles are congruent if in two right-angled triangles, the length of hypotenuse and length of one triangle are equal to the length of the hypotenuse and the length of one side of the other triangle, then the two triangles are congruent.

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Answer

Hint: We need to find the \[\angle C\]. So, we will check the properties of an isosceles trapezium. We will construct a figure of trapezium \[ABCD\] and as in an isosceles trapezium, the base angles are always equal. So, we will construct the figure and name the angles accordingly and then check what is the other base angle with \[\angle C\]. Hence, it depends on how we name an isosceles trapezium. Thus, by this, we can find that \[\angle C\] will be equal to.

Complete step by step solution: We will first construct an isosceles trapezium and name it as \[ABCD\].

Therefore, option C is correct.

Note: We need to remember the properties of an isosceles trapezium and construction of an isosceles trapezium is important. In an isosceles trapezium, consecutive angles along bases are congruent, diagonals are congruent hence, the base angles are always equal.