In trapezoid PQRS, ST=16.1 and PR=33.5. Identify TQ.

Option 2: 17.4

Step-by-step explanation:

PR = SQ = 33.5

SQ = ST + TQ

ST = 16.1 and SQ = 33.5

33.5 = 16.3 + TQ

TQ = 33.5 - 16.1 = 17.4

Step-by-step explanation:

In the given figure:  

 Therefore,    

Given:

So,

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)