Question

A quadrilateral a b c d is inscribed in a circle such that ab is a diameter and angle a d c =130 find angle bac

Answer 1

See the attached file

Answer 2

Answer:

$\angle BAC = 40\degree$

Step-by-step explanation:

Given, ABCD is a cyclic quadrilateral.

AB is a diameter.

$\angle ADC = 130\degree$

$Now, \\\angle B + \angle ADC = 180\degree$

\* We know that,

The pairs of opposite angles of a cyclic quadrilateral are supplementary.*/

$\implies \angle B+130\degree = 180\degree$

$\implies \angle B = 50\degree$

$In \triangle ABC ,\\\angle B=50\degree \\ \angle BCA = 90\degree \: ( Angle\: in\: semicircle )$

$\angle BCA + \angle BAC +\angle B = 180\degree$

/* Angle sum property */

$\implies 90\degree + \angle BAC + 50\degree = 180\degree$

$\implies \angle BAC + 140\degree = 180\degree$

$\implies \angle BAC = 180\degree- 140\degree$

$\implies \angle BAC = 40\degree$

Therefore,

$\angle BAC = 40\degree$

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