Answer:
Part 1) 
Part 2) 
Part 3) 
The answer is the option A
Step-by-step explanation:
Part 1) Find the measure of side HI
Applying the Pythagoras Theorem

substitute the values and solve for HI




Part 2) Find the measure of angle G
In the right triangle GHI

substitute the values


Part 3) Find the measure of angle I
Remember that
The sum of the interior angles of a triangle must be equal to 180 degrees
so

substitute the values


Answer:
x = 6.6
Step-by-step explanation:
Data obtained from the question include the following:
Angle X = 15°
Angle Y° = 23°
Side y = 10
Side x =..?
The value of side x can be obtained by using the sine rule as shown below:
x/Sine X = y/Sine Y
x/Sine 15 = 10/Sine 23
Cross multiply
x × Sine 23 = 10 × Sine 15
Divide both side by Sine 23
x = (10 × Sine 15) / Sine 23
x = 6.6
Therefore, the value of x is 6.6.
All of the centra angles in a regular polygon must add up to 360 degrees. Also, because you're told that it is a regular polygon, the "regular" indicates that all of the central angles will be the same. Divide 360 degrees by 18 degrees to get the number of central angles, which is the same as the number of sides. 360/18 = 20. Therefore, the polygon has 20 sides. Hope that helps!