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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

∵ =

∴ 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°

4

step-by-step explanation:

no solution

step-by-step explanation:

there is not enough information in the problem to solve.