Question

find x in each of the following​

Answer 1

IN first fig x = 32degree

Why: If we join AC we get choprd    and angle X and angle B are angles subtended by the same chords       so they are equal so x = 32degree

In second x = 125degree

Why: ABCD is cyclc quadrialteral that is   angle D + ANgle ABC  =180

ANgle ABC = 180- CBE

Angl;e ABC = 180-55

ANGLE ABC = 125degree

ANgle ABC = 125degree

as Angle D +angle B = 180

x + 125 = 180

x = 180-125

X = 55degre

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Answer 2

1) angle subtended by an arc at the centre is twice the angle subtended by it at any other point of the remaining arc, so

x = 32° x 2 = 64°

2) angle ABC = 180°- 55° = 125°[∡ABC and ∡CBE form a linear pair]

Now, ABCD is a cyclic quadrilateral [Points A, B, C and D are lying on a circle]

So, ∡ABC + x = 180° [Opposite angles of a cyclic quadrilateral are supplementary]

∴ x = 55°

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