Question

Which angles are linear pairs? Check all that apply.
∠SRT and ∠TRV
∠SRT and ∠TRU
∠VRW and ∠WRS
∠VRU and ∠URS
∠URW and ∠WRS

Answer 1

we know that

A linear pair is a pair of adjacent, supplementary angles. Adjacent means next to each other, and supplementary means that the measures of the two angles add up to equal $180$ degrees

So

case a) ∠SRT and ∠TRV

∠$SRT +$∠$TRV=180$°----> by supplementary angles

therefore

∠SRT and ∠TRV is a linear pair

case b) ∠SRT and ∠TRU

∠$SRT +$∠$TRU > 180$°----> are not supplementary angles

therefore

∠SRT and ∠TRU is not a linear pair

case c) ∠VRW and ∠WRS

∠$VRW +$∠$WRS = 180$°----> by supplementary angles

therefore

∠VRW and ∠WRS is a linear pair

case d) ∠VRU and ∠URS

∠$VRU +$∠$URS = 180$°----> by supplementary angles

therefore

∠VRU and ∠URS is a linear pair

case e) ∠URW and ∠WRS

∠$SRT +$∠$TRU < 180$°----> are not supplementary angles

therefore

∠URW and ∠WRS is not a linear pair

Answer 2

∠SRT and ∠TRV form a linear pair  

∠SRT and ∠TRU do not form a linear pair.

∠VRW and ∠WRS form a linear pair.

∠VRU and ∠URS form a linear pair

∠URW and ∠WRS don't form linear pair.

Two angles form a linear pair when they are supplementary in nature i.e. the sum of two angles must be 180° to form a linear pair.

Let us suppose ewe have two angles ∠A and  ∠B such that

∠A +∠B = 180°

then they form a linear pair.

In such a case ∠A and ∠B are called supplementary angles.

∠A and  ∠B together form a line hence also called as linear pair.

Checking the above condition for all the options given

∠SRT and ∠TRV

∠SRT + ∠TRV =180°

hence ∠SRT and ∠TRV form a linear pair  

 

∠SRT and ∠TRU

∠SRT + ∠TRU $\neq$ 180°

hence ∠SRT and ∠TRU do not form a linear pair.

∠VRW and ∠WRS

∠VRW + ∠WRS =  180°

hence ∠VRW and ∠WRS form a linear pair.

∠VRU and ∠URS

∠VRU + ∠URS= 180°

hence ∠VRU and ∠URS form a linear pair

∠URW and ∠WRS

∠URW + ∠WRS ≠ 180°

hence ∠URW and ∠WRS don't form linear pair.

For more information please refer to the link below

https://brainly.com/question/13045673