1 Answer

Learning Curve · Answer 1 · 2023-07-25T17:26:37+0000

Answer:

$\implies m\angle A =42\degree$

Explanation:

Quadrilateral ABCD is inscribed in circle with center O.

-> Quadrilateral ABCD is cyclic.

Opposite angles of a cyclic quadrilateral are supplementay.

$\implies m\angle B + m\angle D = 180\degree$

$\implies (2x)\degree + (3x-5)\degree = 180\degree$

$\implies (5x-5)\degree = 180\degree$

$\implies 5x-5= 180$

$\implies 5x= 185$

$\implies x= (185)/(5)$

$\implies x= 37$

$\implies m\angle A =(x+5)\degree$

$\implies m\angle A =(37+5)\degree$

$\implies \huge{\orange{m\angle A =\boxed{42}\degree}}$

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