The value of the variable <em>x</em> can be determined using the circle theorem to 
determine the angle formed by <em>x</em>.
The correct responses are;
Reasons:
(1) From circle theorem, we have; 
- Equal chords subtends equal arcs and vice versa
- Equal chords subtend equal angles at the center of a circle
Therefore;
Angle subtended by  at center = Angle subtended by
 at center = Angle subtended by  at the center;
 at the center;
- Angle at the center = 2 × Angle at the circumference
Therefore;
Angle subtended by  at the circumference = Angle subtended by
 at the circumference = Angle subtended by  at the circumference
 at the circumference
Which gives;
(2)  given
 given
Angle subtended by arc  at the center = x
 at the center = x
Equal arcs subtend equal angles at the center of a circle.
Therefore;
Angle subtended by arc  at the center = x
 at the center = x
Angle at center = 2 × angle at circumference
Therefore;
x = 2 × 50° = 100°
x = <u>100°</u>
 
(3)  given
 given
By definition, we have;
Angle subtended by  at the center = 3 × Angle subtended by
 at the center = 3 × Angle subtended by  at the center
 at the center
According to circle theorem, we have;
Angle at the center = 2 × Angle at the circumference
Let <em>y</em> represent the angle subtended at the circumference by  , we have;
, we have;
y = 20°
 = 2·y
 = 2·y
 = 3 ×
 = 3 ×  = 3 × 2·y = 6·y
 = 3 × 2·y = 6·y
Therefore;
 = 6 × 20° = 120°
 = 6 × 20° = 120°
 = 120°
 = 120°
 = 2·x
 = 2·x
Therefore;
2·x = 120°

x = <u>60°</u>
Learn more circle theorems here:
brainly.com/question/16879446
 
        
                    
             
        
        
        
Answer:
11:4
Step-by-step explanation:
Hello. All you have to do here is make it as a fraction, so it would be people at the round-up to people at the slingshot. Really it would be a fraction, but on this question it wants a ratio. Hopefully you understand! :D
 
        
                    
             
        
        
        
Answer:
m∡A = 41.4° 
m∡B = 48.6°
m∡C = 90°
a = 3
b = 9
c = 12
Step-by-step explanation:
to find the length of side 'a' I used the Pythagorean Theorem to get:
a² + 9² = 12²
a² + 81 = 144
a² = 63
a =  which equals
 which equals 
 which is 3
 which is 3
to find m∡B I found the arcsin(B) = 9/12 to get 48.6
to find m∡A I subtracted the sum of 90 + 48.6 from 180°