Question

complementary and supplementary angles
assignment active
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.
$mangle hnk + mangle knl = 180^circ$
$mangle mng + mangle gnh = 90^circ$

Explanation:

Step1: Define complementary/supplementary

Complementary: sum = $90^\circ$; Supplementary: sum = $180^\circ$

Step2: Check ∠GNH & ∠HNJ

$\angle GNH + \angle HNJ = 90^\circ$ (right angle given). True.

Step3: Check ∠JNK & ∠KNL

$\angle JNK + \angle KNL
eq 180^\circ$. False.

Step4: Check ∠KNL & ∠LNM

$\angle KNL + \angle LNM = 90^\circ$ (right angle). True.

Step5: Check $m\angle HNK + m\angle KNL$

$\angle HNK + \angle KNL = 180^\circ$ (straight line). True.

Step6: Check $m\angle MNG + m\angle GNH$

$\angle MNG + \angle GNH = 180^\circ - 90^\circ = 90^\circ$. True.

Answer:

• $\angle$GNH and $\angle$HNJ are complementary.
• $\angle$KNL and $\angle$LNM are complementary.
• $m\angle HNK + m\angle KNL = 180^\circ$
• $m\angle MNG + m\angle GNH = 90^\circ$