Question

find m∠f in rhombus defg.

m∠f = \boxed{}°
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Explanation:

Step1: Use rhombus opposite angles property

In a rhombus, opposite angles are equal, so $\angle E = \angle G$.
$4b - 98 = 2b - 22$

Step2: Solve for $b$

Subtract $2b$ and add 98 to both sides:
$4b - 2b = -22 + 98$
$2b = 76$
$b = 38$

Step3: Calculate $m\angle E$

Substitute $b=38$ into $\angle E$:
$m\angle E = 4(38) - 98 = 152 - 98 = 54^\circ$

Step4: Use consecutive angles supplementary property

In a rhombus, consecutive angles are supplementary, so $m\angle E + m\angle F = 180^\circ$.
$m\angle F = 180 - 54$

Answer:

$126$