In the below figure=y ????
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i tried to explain in simple way hope it will help you
Given: [tex]\[\angle AOC = {x^ \circ },\angle COD = {90^ \circ },\angle DOB = {y^ \circ },\angle AOE = 3{x^ \circ },\angle EOB = {72^ \circ }\][/tex]
To find: The measure of angle y.
Solution:
Note that, in order to find the value of angle y. First, find the value of x.
Find the value of x.
[tex]\[\angle AOE + \angle EOB = {180^ \circ }\][/tex] (linear pair)
[tex]\[\begin{array}{l} \Rightarrow 3{x^ \circ } + {72^ \circ } = {180^ \circ }\\ \Rightarrow 3{x^ \circ } = {180^ \circ } - {72^ \circ }\\ \Rightarrow 3{x^ \circ } = {108^ \circ }\end{array}\][/tex]
[tex]\[\begin{array}{l} \Rightarrow x = \frac{{108}}{3}\\ \Rightarrow x = {36^ \circ }\end{array}\][/tex]
Find the measure of angle y.
[tex]\[\angle AOC + \angle COD + \angle DOB = {180^ \circ }\][/tex]
[tex]\[\begin{array}{l} \Rightarrow {x^ \circ } + {90^ \circ } + {y^ \circ } = {180^ \circ }\\ \Rightarrow {36^ \circ } + {90^ \circ } + {y^ \circ } = {180^ \circ }\\ \Rightarrow {126^ \circ } + {y^ \circ } = {180^ \circ }\end{array}\][/tex]
[tex]\[\begin{array}{l} \Rightarrow {y^ \circ } = {180^ \circ } - {126^ \circ }\\ \Rightarrow y = {54^ \circ }\end{array}\][/tex]
Hence, the measure of ange y is [tex]54^ \circ[/tex].