Question

1. solve for x.

(a) if x=180° draw
a half moon in the
background.
(b) if x=60° draw a
full moon in the
background.
solve for x. 128°

Explanation:

Step1: Analyze the circle's angle sum

A full circle has a total angle of \( 360^\circ \), but here we have a straight line (diameter) which forms a \( 180^\circ \) angle with the two sectors. So the sum of the angles \( 2x \) and \( x \) should equal \( 180^\circ \) (since they are on a straight line through the center).

Step2: Set up the equation

We set up the equation \( 2x + x = 180^\circ \). Combining like terms, we get \( 3x = 180^\circ \).

Step3: Solve for \( x \)

To solve for \( x \), we divide both sides of the equation by 3: \( x=\frac{180^\circ}{3}=60^\circ \).

Answer:

\( x = 60^\circ \)