Question

find ( mangle g ) and ( mangle f ) in rhombus ( defg ).
( mangle g = square^circ )
( mangle f = square^circ )

Explanation:

Step1: Use rhombus consecutive angles property

Consecutive angles in a rhombus are supplementary, so:
$$(7s+51) + (4s+8) = 180$$

Step2: Simplify and solve for s

Combine like terms and isolate s:
$$11s + 59 = 180$$
$$11s = 180 - 59$$
$$11s = 121$$
$$s = \frac{121}{11} = 11$$

Step3: Calculate $m\angle G$

Substitute $s=11$ into $\angle G$ expression:
$$m\angle G = 4(11) + 8 = 44 + 8 = 52$$

Step4: Calculate $m\angle F$

Opposite angles in a rhombus are equal, so $m\angle F = m\angle D$:
$$m\angle F = 7(11) + 51 = 77 + 51 = 128$$

Answer:

$m\angle G = 52^\circ$
$m\angle F = 128^\circ$