Question

PLS, HELP WILL GIVE BRAINLIEST, THANKS, AND 5 STAR RATING TO ANSWER SHOWING ALL WORK.

Answer 1

Answer:

Step-by-step explanation:

1. Opposite angles are supplementary

A+C = 180

A = 180-121 = 59

2. Opposite angles are supplementary

A+C = 180

3x+6+x+2 = 180

4x+8 = 180

4x = 172

x = 43

A = 3x+6 = 3(43)+6

= 135

3. Opposite angles are supplementary

B+D = 180

28+x = 180

x = 152

A = x-36 = 152-36

= 116

4. Opposite angles are supplementary

f+90 = 180

f = 90

Central angle = 2x inscribed angle = 2x75 = 150

Sum of central angles = 360

150+110+g = 360

g = 360-150-110 = 100

5. Opposite angles are supplementary

S+V = 180

x+77+x+103=180

2x+180=180

x=0

S=77

Central angle = 2x inscribed angle = 2x77 = 154

Sum of central angles = 360

mRST+154 = 360

mRST = 360-154 = 206

Answer 2

Answer:

(a) ∠DAB  = 59°

(b) ∠A  = 135°

(c)  ∠A   = 99°

Step-by-step explanation:

Theorem: 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°

(4)