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 = 1.3 in. EG = 3 in. m∠X = ° m∠G = °

The answer is given below

Step-by-step explanation:

In triangle EFG, let a = EG, A = ∠f, b= 1.3 in, B = ∠G, c = 2.4 in C = ∠E = 48°

Using cosine rule:

EG = 3 inches

Using sine rule,

∠G = B = 23.7°

Given ΔXYZ ≅ ΔEGF,

Therefore: ZX = EF = 1.3 inches, m∠X = m∠G =23.7 °, m∠Z = m∠F = 107°

ZY = FG = 2.4

ZX = 1.3 in.

EG = 3 in.

m∠X = 48°

m∠G = 25°

Step-by-step explanation:

ΔXYZ ≅ ΔEGF

107 + 48 = 155

m∠G = 180 - 155 = 25