Question

these figures are congruent. what is ( mangle i )?

Explanation:

Step1: Sum quadrilateral interior angles

The sum of interior angles of a quadrilateral is $(4-2)\times180^\circ = 360^\circ$.

Step2: Identify congruent angle pairs

Since the quadrilaterals are congruent, $\angle G \cong \angle L$, $\angle H \cong \angle N$, $\angle F \cong \angle M$, so $\angle I \cong \angle K$.

Step3: Calculate $m\angle I$

Subtract known angles from total:
$m\angle I = 360^\circ - 67^\circ - 138^\circ - 61^\circ$
$m\angle I = 360^\circ - (67^\circ + 138^\circ + 61^\circ)$
$m\angle I = 360^\circ - 266^\circ = 94^\circ$

Answer:

$94^\circ$