Question

foundations of euclidean geometry. in the diagram, which angles form a linear pair? choose three correct answers. ∠rst and ∠rsv. ∠rst and ∠vsu. ∠rst and ∠tsu. ∠tsu and ∠usv. ∠tsu and ∠rsv

Explanation:

Step1: Recall linear - pair definition

Two angles form a linear pair if they are adjacent and their non - common sides are opposite rays.

Step2: Analyze each option

• For ∠RST and ∠RSV: They share side RS, and non - common sides ST and SV are not opposite rays.
• For ∠RST and ∠VSU: They are not adjacent.
• For ∠RST and ∠TSU: They share side ST, and non - common sides RS and SU are opposite rays, so they form a linear pair.
• For ∠TSU and ∠USV: They share side SU, and non - common sides ST and SV are opposite rays, so they form a linear pair.
• For ∠TSU and ∠RSV: They are not adjacent.

Answer:

∠RST and ∠TSU, ∠TSU and ∠USV