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Quadrilateral ABCD is inscribed In a circle.
What is the measure of angle A?

Quadrilateral ABCD Is Inscribed In A Circle What Is The Measure Of Angle A class=

Sagot :

Hrishii

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]

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