Question

Triangles X Y Z and E G F are shown. Side X Y is 3.0 inches and angle Y Z X is 107 degrees. Side F G is 2.4 inches and side E F is 1.3 inches. Angle G E F is 48 degrees.
Given ΔXYZ ≅ ΔEGF, find the measurements of the unknown sides and angles.

ZX =
in.

EG =
in.

m∠X =
°

m∠G =
°

Answer 1

From the correspondence ΔXYZ ≅ ΔEGF, X↔E, Y↔G, Z↔F.

- ZX corresponds to EF, so ZX = 1.3 in.
- EG corresponds to XY, so EG = 3.0 in.
- m∠X = m∠E = 48° (given angle GEF = 48°).
- m∠G = m∠Y. Since m∠Z = 107° and m∠X = 48°, m∠Y = 180° − 107° − 48° = 25°, so m∠G = 25°.

Answers:
ZX = 1.3 in
EG = 3.0 in
m∠X = 48°
m∠G = 25°