Question

in the image shown, (overleftrightarrow{pf} parallel overleftrightarrow{yk}), where (mangle phm = (11z + 6)^circ), (mangle mhx = 47^circ), and (mangle hwr = 72^circ). the value of (z) is (6^circ) , with a measure of (angle fhr) of (108^circ) and a measure of (angle gwr) of

Explanation:

To find \( m\angle GWR \), we can use the property of supplementary angles (since \( \angle HWR \) and \( \angle GWR \) form a linear pair, their sum is \( 180^\circ \)).

Step 1: Recall the linear pair property

If two angles form a linear pair, they are supplementary, meaning their measures add up to \( 180^\circ \). So, \( m\angle HWR + m\angle GWR = 180^\circ \).

Step 2: Substitute the known value

We know \( m\angle HWR = 72^\circ \). Substitute this into the equation:
\( 72^\circ + m\angle GWR = 180^\circ \)

Step 3: Solve for \( m\angle GWR \)

Subtract \( 72^\circ \) from both sides:
\( m\angle GWR = 180^\circ - 72^\circ = 108^\circ \)

Answer:

\( 108^\circ \)