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aliya0001 [1]
2 years ago
14

Find the measure of the unknown angle.

Mathematics
2 answers:
Alecsey [184]2 years ago
5 0

Answer:

The answer is in the screenshot provided.

Step-by-step explanation:

Tomtit [17]2 years ago
4 0

Answer:

131° Degrees

Step-by-step explanation:

It's the same just put in different places

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(a) ∠DAB  = 59°

(b) ∠A  = 135°

(c)  ∠A   = 99°

Step-by-step explanation:

<u>Theorem</u>: If a quadrilateral is inscribed inside a circle, then the opposite angles of the quadrilateral are SUPPLEMENTARY.

So, here in the given figures:

(1) ∠DCB +   ∠DAB  = 180°  (as opposite angles are supplementary)

⇒∠DAB   =  180°  -   121°   =  59°

or, ∠DAB  = 59°

(2) ∠DCB +   ∠DAB  = 180°  (as opposite angles are supplementary)

⇒(3x+6) + (x+2) = 180° or, 4x = 180 - 8 = 172

⇒ x = 172/4 = 43, or x  = 43

So, ∠A  = (3x+6)  =  3(43) + 6 = 135°

(3) (28) +  (x) = 180°

or, x =  180 - 28 = 152

So, ∠A  = (x- 36)  =  135 - 36  = 99°

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