Question

determining angle relationships in a diagram. which statements are true regarding the diagram? choose three correct answers. m∠mng + m∠gnh = 90°. ∠knl and ∠lnm are complementary. m∠hnk + m∠knl = 180°. ∠gnh and ∠hnj are complementary.

Explanation:

Step1: Recall angle - relationship definitions

Complementary angles add up to 90°, and supplementary angles add up to 180°.

Step2: Analyze the first option

Since ∠MNG and ∠GNH form a right - angle at N, \(m\angle MNG + m\angle GNH=90^{\circ}\). This is true.

Step3: Analyze the second option

∠KNL and ∠LNM do not form a right - angle. They are not complementary. This is false.

Step4: Analyze the third option

∠HNK and ∠KNL form a straight - line at N. So, \(m\angle HNK + m\angle KNL = 180^{\circ}\). This is true.

Step5: Analyze the fourth option

∠GNH and ∠HNJ form a right - angle at N. So, ∠GNH and ∠HNJ are complementary. This is true.

Answer:

1. \(m\angle MNG + m\angle GNH = 90^{\circ}\)
2. \(m\angle HNK + m\angle KNL = 180^{\circ}\)
3. ∠GNH and ∠HNJ are complementary