Question

answer the question​

Answer 1

$\bold{Solution:}$

$\implies \sf \angle\;XYZ\;+\angle\;ZYP= 180^{\circ}\quad [L.P]$

$\sf \implies 64^{\circ}+\;\angle\;ZYP=180^{\circ}$

$\sf \implies \angle\;ZYP=180^{\circ}-64^{\circ}$

$\sf \implies \angle\;ZYP=116^{\circ}$

$\sf \therefore \angle\;XYQ=\angle\;XYZ+\angle\;ZYQ$

$\sf \implies 64+58\\ \\ \implies 122.\quad{Ans.}$

$\sf \therefore\;Reflex\;of\;\angle\;QYP = 360-58\\ \\ \implies Ans. = 302^{\circ}$

If,

AB || CD and transversal T intersect then out at P and Q respect.

$\bold{Therefore\;1\;pair\;of\;corresponding\;angles\;are\;equal.}$

$\sf \implies \angle\;1=\;\angle\;5\\ \implies \angle\;2=\angle\;6.\\ \\ \implies \angle\;3=\angle\;7\\ \\ \implies \angle\;4=\angle\;8.$

$\bold{Therefore\;2\;pair\;of\;alternate\;interior\;angles\;are\;equal.}$

$\sf \implies \angle\;3=\angle\;5\\ \\ \implies \angle\;4=\angle\;6.$

$\bold{Therefore\;3\; pair\; of\;consecutive\;interior\;angles\;are\;supplementary.}$

$\sf \implies \angle\;4+\angle\;5=180^{\circ}\\ \\ \implies \angle\;3+\angle\;6=180^{\circ}$