Step-by-step explanation:
Given the two triangles, ΔFEG (and its two angles that have measures of 30° and 102°) and ΔNLM (whose two angles have measures of 48° and 102°).
We can start by using the Angle Angle (AA) criterion, which states that if a triangle has two angles whose measures are equal to the two angles of a second triangle, then those two triangles are similar.
Since we know that the sum of the interior angles of a triangle is 180°, we can determine the missing angles for Δ FEG and ΔNLM. In doing so, we'll be able to find out if both triangles have two equal angles.
Find m < G° for Δ FEG:
m < G° = 180° - 102° - 30°
m < G° = 48°.
Find m < M for ΔNLM:
m< M° = 180° - 102° - 48°
m < M° = 30°.
With our calculations on the measures of the missing angles of each triangle, it turns out that the interior angles of ΔFEG and ΔNLM have the same measures:
< E = < L ⇒ 102°
< N = < G ⇒ 48°
< F = < M ⇒ 30°
Therefore, ΔFEG and ΔNLM are similar, as defined by the Angle Angle (AA) criterion.
