Question

ABCD is a cyclic quadrilateral in which AB∥ . If ∠ D = 70°, find all the remaining angles. (draw with figure)​

Answer 1

Answer:

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>>ABCD is a cyclic quadrilateral whose dia

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ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ΔDBC=70

o

, ΔBAC is 30

o

, find ∠ BCD. Further if AB=BC, find ∠ ECD.

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Solution

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For chord CD,

∠CBD=∠CAD ...Angles in same segment

∠CAD=70°

∠BAD=∠BAC+∠CAD=30°+70°=100°

∠BCD+∠BAD=180° ...Opposite angles of a cyclic quadrilateral

⇒∠BCD+100°=180°

⇒∠BCD=80°

In △ABC

AB=BC (given)

∠BCA=∠CAB ...Angles opposite to equal sides of a triangle

Answer 2

ABCD is a cyclic quadrilateral in which ab is parallel to CD

And angle d is equal to 70 degree

Angle (B + d) = 180

Angle B + 70 = 180

Angle B = 180 - 70

Angle B = 110

AB ll CD

Angle ( A + D ) = 180 (Co interior angle)

Angle A = 180 - 70

Angle A = 110

Angle (B+c)= 180 (co interior angle

Angle C = 180 - 110

Angle c = 70

hence angle A will be equal to 110 degree angle B will be equal to 110 degree and Angle C will be equal to 70 degree

Thanks