L U C K luck is parallelogram with ∠C=68° and ∠LUK=42° find: 1.
m∠ CUK 2. m∠ K

1. m∠CUK = 70°

2. m∠K = 112°

Step-by-step explanation:

1. The given parameters of the parallelogram LUCK are;

∠C = 68°

∠LUK = 42°

From the diagram of parallelogram LUCK obtained from an online source, we have;

Given that LUCK = A parallelogram, we have;

The same side interior angles ∠C and ∠U are supplementary angles

Therefore;

∠C + ∠U = 180°

∠U = 180° - ∠ C

∴ ∠U = 180° - 68° = 112°

∠U = 112°

By angle addition property, ∠U = ∠LUK + ∠CUK

∴ m∠CUK = ∠U - ∠LUK

By plugging in the value of ∠LUK = 42°, and ∠U = 112°, we have;

m∠CUK = ∠U - ∠LUK = 112° - 42° = 70°

m∠CUK = 70°

2. By angle addition property, we have;

∠K = ∠LKU + ∠CKU

∠LKU and ∠CUK are alternate interior angles

∴ ∠LKU = ∠CUK = 70°

Similarly, ∠CKU and ∠LUK are alternate interior angles

∠CKU = ∠LUK = 42°

m∠K = ∠LKU + ∠CKU = 70° + 42° = 112°

m∠K = 112°.

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