Question

Which statements are true regarding the diagram? GNH and HNJ are complementary. JNK and KNL are supplementary. KNL and LNM are complementary. mHNK + mKNL = 180° mMNG + mGNH = 90°

Answer 1

Answer:

Step-by-step explanation:

Since we want to know which statements are true regarding the diagram? GNH and HNJ are complementary. JNK and KNL are supplementary. KNL and LNM are complementary. mHNK + mKNL = 180° mMNG + mGNH = 90°.

Lets consider the diagram bellow.

Since ∠GNJ and ∠JNK form a straight angle and ∠JNK = 90°, we can conclude that ∠GNJ = 90°.

Thus ∠GNH + ∠HNJ = 90°.

Hence we have that ∠GNH and ∠HNJ are complimentary.

Since JNK and KNL do not form a straight angle, we conclude that

∠JNK + ∠KNL is not equal to 180°.

Hence the statement that says that ∠JNK and ∠KNL are supplementary is not true.

Since ∠KNM and ∠JNK form a straight angle and ∠JNK = 90° we conclude that <KNM = 90°.

So ∠KNL + ∠LNM = 90°

Thus ∠KNL and ∠LNM are complimentary.

Since ∠HNL makes a straight angle, we get that ∠HNK + ∠KNL = 180°.

Since ∠MNG itself is 90°, hence ∠MNG + ∠GNH can not be 90° hence this is false.

Answer 2

Answer:

GNH and HNJ are complementary.

KNL and LNM are complementary.

HNK + KNL = 180°

Step-by-step explanation:

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