Question

= 29.3°
dx = 20.6°
ractive diagram to determine ( moverarc{gx} ).
( mangle gdx )
( moverarc{mb} )
( moverarc{gx} )
measure
20.6°
29.3°
reason
given
given
the ( moverarc{gx} ) is
reason:

Explanation:

Step1: Recall the theorem for angle formed by two secants

The measure of an angle formed by two secants outside a circle is half the difference of the measures of the intercepted arcs. The formula is \( m\angle GDX=\frac{1}{2}(m\widehat{GX}-m\widehat{MB}) \).

Step2: Substitute the known values

We know \( m\angle GDX = 20.6^{\circ} \) and \( m\widehat{MB}=29.3^{\circ} \). Substitute these into the formula:
\( 20.6^{\circ}=\frac{1}{2}(m\widehat{GX}-29.3^{\circ}) \)

Step3: Solve for \( m\widehat{GX} \)

Multiply both sides by 2:
\( 2\times20.6^{\circ}=m\widehat{GX}-29.3^{\circ} \)
\( 41.2^{\circ}=m\widehat{GX}-29.3^{\circ} \)

Add \( 29.3^{\circ} \) to both sides:
\( m\widehat{GX}=41.2^{\circ}+29.3^{\circ} \)
\( m\widehat{GX}=70.5^{\circ} \)

Answer:

The \( m\widehat{GX} \) is \( 70.5^{\circ} \). Reason: The measure of an angle formed by two secants outside a circle is half the difference of the measures of the intercepted arcs (\( m\angle GDX=\frac{1}{2}(m\widehat{GX}-m\widehat{MB}) \)), and solving the equation gives \( m\widehat{GX} = 70.5^{\circ} \).