Questions: Determining Angle Relationships in a Diagram Which statements are true regarding the diagram? angle GNH and angle HNJ are complementary. angle JNK and angle KNL are supplementary. angle KNL and angle LNM are complementary. m(angle) HNK + m(angle) KNL = 180 degrees m(angle) MNG + m(angle) GNH = 90 degrees

Determining Angle Relationships in a Diagram

Which statements are true regarding the diagram?
angle GNH and angle HNJ are complementary.
angle JNK and angle KNL are supplementary.
angle KNL and angle LNM are complementary.
m(angle) HNK + m(angle) KNL = 180 degrees
m(angle) MNG + m(angle) GNH = 90 degrees

Transcript text: Determining Angle Relationships in a Diagram Which statements are true regarding the diagram? $\angle \mathrm{GNH}$ and $\angle \mathrm{HNJ}$ are complementary. $\angle \mathrm{JNK}$ and $\angle \mathrm{KNL}$ are supplementary. $\angle \mathrm{KNL}$ and $\angle \mathrm{LNM}$ are complementary. $m_{\angle} \mathrm{HNK}+m_{\angle} \mathrm{KNL}=180^{\circ}$ $m_{\angle} \mathrm{MNG}+m_{\angle} \mathrm{GNH}=90^{\circ}$

Solution

Solution Steps

Step 1: Identify Complementary Angles

Complementary angles are two angles whose measures add up to 90 degrees. In the diagram, ∠GNH and ∠HNJ are adjacent and form a right angle at point N. Therefore, they are complementary.

Step 2: Identify Supplementary Angles

Supplementary angles are two angles whose measures add up to 180 degrees. In the diagram, ∠JNK and ∠KNL are adjacent and form a straight line at point N. Therefore, they are supplementary.

Step 3: Identify Another Pair of Complementary Angles

Complementary angles are two angles whose measures add up to 90 degrees. In the diagram, ∠KNL and ∠LNM are adjacent and form a right angle at point N. Therefore, they are complementary.