Question

in the diagram, which two angles are adjacent?

∠smd and ∠kms
∠deq and ∠tig
∠mkt and ∠njt
∠njg and ∠njf

the three vertices of △abc are in quadrant i. if △abc is reflected in the x - axis, its image will lie in quadrant
i
iv
ii
iii

Explanation:

Step1: Recall adjacent - angle definition

Adjacent angles share a common side and a common vertex and have no interior points in common.

Step2: Analyze each option

• For $\angle SMD$ and $\angle KMS$, they share side $MS$ and vertex $M$, and have no interior - points in common.
• $\angle DEQ$ and $\angle TIG$ are not adjacent as they are far apart and have no common side or vertex.
• $\angle MKT$ and $\angle NJT$ have no common side or vertex.
• $\angle FJG$ and $\angle NJF$ have no common side or vertex.

Step3: Recall reflection rule

When a point $(x,y)$ is reflected over the $x$ - axis, the new point is $(x, - y)$.

Step4: Determine the quadrant

If $\triangle ABC$ has vertices in Quadrant I (where $x>0$ and $y > 0$), after reflection over the $x$ - axis, the $x$ - coordinates remain positive and the $y$ - coordinates become negative. So the image lies in Quadrant IV.

Answer:

1. $\angle SMD$ and $\angle KMS$
2. IV