Question

which of the following is correct?
∠pjk and ∠pjm are adjacent and also supplementary.
∠kjm is acute. also, ∠pjm is obtuse.
∠ljm is a straight angle. also, ∠ljn is obtuse.
∠ljp is a right angle. also, ∠pjk and ∠kjm are complementary.

Explanation:

Step1: Analyze each option

• Option 1: $\angle{PJK} = 46^{\circ}$, $\angle{PJM}=46^{\circ}+90^{\circ}=136^{\circ}$. They are not adjacent.
• Option 2: $\angle{KJM}=44^{\circ}$ (acute), $\angle{PJM}=44^{\circ}+90^{\circ}=134^{\circ}$ (obtuse).
• Option 3: $\angle{LJM}$ is not a straight angle. A straight angle is $180^{\circ}$, and from the figure, $\angle{LJM}$ is not formed in that way.
• Option 4: $\angle{LJP}$ is a right angle. $\angle{PJK} = 46^{\circ}$, $\angle{KJM}=44^{\circ}$, $46^{\circ}+44^{\circ}=90^{\circ}$, so they are complementary.

Answer:

$\angle{LJP}$ is a right angle. Also, $\angle{PJK}$ and $\angle{KJM}$ are complementary.