Answer:
m∠W is 28°
m∠X is 24°
Step-by-step explanation:
In any triangle, the measure of an exterior angle at one vertex of a triangle equals the sum of the measures of the two interior angles opposite to this vertex
In the given figure
∵ ∠WYZ is an exterior angle of Δ XYW at vertex Y
∵ ∠W and ∠X are the interior angles of Δ XYW opposite to the vertex Y
→ Use the fact above
∴ m∠WYZ = m∠X + m∠W
∵ m∠WYZ = 52°
∵ m∠X = 3y°
∵ m∠W = (4y - 4)°
→ Substitute them in the equation above
∵ 52 = 3y + 4y - 4
→ Add the like terms
∴ 52 = 7y - 4
→ Add 4 to both sides
∵ 52 + 4 = 7y - 4 + 4
∴ 56 = 7y
→ Divide both sides by 7
∵ [tex]\frac{56}{7}[/tex] = [tex]\frac{7y}{y}[/tex]
∴ 8 = y
→ Substitute y in the measures of ∠X and ∠W
∵ m∠X = 3(8)
∴ m∠X = 24°
∵ m∠W = 4(8) - 4 = 32 - 4
∴ m∠W = 28°
