Question

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

Explanation:

Step1: Identify congruent triangle angles

Congruent triangles have matching angles. In triangle STU, $\angle S = 42^\circ$, $\angle T = 60^\circ$, $\angle U = 78^\circ$.

Step2: Match angles in triangle EFG

In $\triangle EFG$, $\angle E = 60^\circ$ (matches $\angle T$), $\angle F = 78^\circ$ (matches $\angle U$). Thus $\angle G$ matches $\angle S$.

Step3: Verify with triangle angle sum

Sum of angles in a triangle is $180^\circ$. Calculate $\angle G$:
$\angle G = 180^\circ - 60^\circ - 78^\circ = 42^\circ$

Answer:

$42$