Answer:
[tex] m\angle A = 133\degree [/tex]
Step-by-step explanation:
Quadrilateral ABCD is inscribed In a circle.
So, ABCD is a cyclic Quadrilateral.
Opposite angles of a cyclic quadrilateral are supplementary.
Therefore,
(4x + 5)° + (x + 15)° = 180°
(4x + 5 + x + 15)° = 180°
(5x + 20)° = 180°
5x + 20 = 180
5x = 180 - 20
5x = 160
x = 160/5
x = 32
[tex] m\angle A = (4x + 5)\degree [/tex]
[tex] m\angle A = (4\times 32+ 5)\degree [/tex]
[tex] m\angle A = (128+ 5)\degree [/tex]
[tex] m\angle A = 133\degree [/tex]
