3 years ago

Add. Write in simplest form.-4/5 + (-3/8)

Mathematics

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oee [108]3 years ago

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Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.

LuckyWell [14K]

Step-by-step explanation:

Quadrilateral ABCD is inscribed in a circle.

Opposite angles of a Quadrilateral are Supplementary.

$\therefore \: \angle A + \angle C = 180° \\ \therefore \:(2x + 3) \degree+ (2x + 1) \degree = 180° \\ \therefore \: (4x + 4) \degree = 180° \\ \therefore \: (4x + 4) = 180 \\ \therefore \: 4x = 180 - 4 \\ \therefore \: 4x = 176 \\ \therefore \: x = \frac{176}{4} \\ \therefore \: x = 44 \\ \\ m\angle A = (2x + 3) \degree \\ = (2 \times 44 + 3) \degree \\ = (88 + 3) \degree \\ \huge \red{ \boxed{ \therefore \: m\angle A =91 \degree}} \\ \\ m\angle C = (2x + 1) \degree \\ = (2 \times 44 + 1) \degree \\ = (88 + 1) \degree \\ \huge \red{ \boxed{ \therefore \: m\angle C=89\degree}} \\ \\ m\angle D= (x - 10) \degree \\ = (44 - 10) \degree \\ \huge \red{ \boxed{ \therefore \: m\angle D =34\degree}} \\ \\ similarly \\ \\ \huge \red{ \boxed{ \therefore \: m\angle B = 146\degree}} \\ \\$