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Given AB¯CD¯;mD=116;AKbisects mDAB

  1. Find the measures of DAB,KABandDKA
  2. Is there enough information for you to conclude thatD andCare supplementary, or is more information needed?



Short Answer

Expert verified

a. Measurement of angles aremDAB=64,mKAB=32andmDKA=32

b.More information is needed to conclude thatD andC are supplementary.

Step by step solution

01

Part a. Step 1. Find ∠DAB.

Line segmentDA¯ is transversal to the parallel linesAB¯ andCD¯

DABandCDA forms a pair of same-side interior angles

Theorem 3-3: If two parallel lines are cut by a transversal then the same-side interior angles are supplementary.

mDAB+mCDA=180mDAB+116=180mDAB=180116mDAB=64

02

Part a. Step 2. Find ∠KAB.

Since, AKbisects DAB. So KABis half of angle DAB

KAB=DAB2KAB=642KAB=32

03

Part a. Step 3. Find ∠DKA.

Line segmentAK is transversal to the parallel linesAB¯ andCD¯

KABandDKA forms a pair of alternate interior angles

Theorem 3-2: If two parallel lines are cut by a transversal then the alternate interior angles are congruent.

DKAKABmDKA=mKABmDKA=32

Thus,mDAB=64,mKAB=32andmDKA=32

04

Part b. Step 1. Observations from figure.

Line segmentsDA¯andBC¯ are transversal to the parallel linesAB¯ andCD¯

05

Part b. Step 2. Angles which can be find using given information.

Angles which can be find areDAB,KAB,KAD,andDKA

06

Part b. Step 3. Angles which cannot be find using given information.

Angles which cannot be find are AKB,KBA,KBC,BKC,andKCB

Thus, to find Cmore information is needed.

Hence, we cannot conclude thatD andC are supplementary.

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