Find the value of z , y , z in the diagram .
No spam otherwise I will report that question .
Ok
Share
Find the value of z , y , z in the diagram .
No spam otherwise I will report that question .
Ok
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Verified answer
Step-by-step explanation:
this is your answer in the above picture.
Given:
Find:
Solution:-
In line segment AB
[tex]\sf \to\angle AOC +\angle DOC + \angle DOB = 180^{\circ}\quad\bigg\lgroup Linear\:Pair\bigg\rgroup \\ [/tex]
[tex]\sf where \small{\begin{cases} \sf\angle AOC = 2x \\ \sf\angle DOC = {90}^{ \circ} \\ \sf\angle DOB = x\end{cases}}[/tex]
[tex]\bigstar[/tex] Substituting these values:-
[tex]\sf \implies\angle AOC +\angle DOC + \angle DOB = 180^{\circ} \\ \\ [/tex]
[tex]\sf \implies 2x +90+ x = 180\\ \\ [/tex]
[tex]\sf \implies 3x +90 = 180\\ \\ [/tex]
[tex]\sf \implies 3x= 180 - 90\\ \\ [/tex]
[tex]\sf \implies 3x=90\\ \\ [/tex]
[tex]\sf \implies x= \dfrac{90}{3}\\ \\ [/tex]
[tex]\sf \implies x= {30}^{ \circ}\\ \\ [/tex]
[tex] \underline{\boxed{ \sf\therefore Value\:of\:x\:is\:30^{\circ}}}[/tex]
Now,
[tex]\sf \to \angle AOC = \angle EOB\quad\bigg\lgroup Vertical\:Opposite\: Angles\bigg\rgroup \\ [/tex]
[tex]\sf where \small{\begin{cases} \sf\angle AOC =2x \\ \sf \angle EOB = y \\ \sf x = {30}^{ \circ} \end{cases}}[/tex]
[tex]\bigstar[/tex] Substituting these values:-
[tex]\sf \implies\angle AOC = \angle EOB \\ \\ [/tex]
[tex]\sf \implies 2x = y \\ \\ [/tex]
[tex]\sf \implies 2(30) = y \\ \\ [/tex]
[tex]\sf \implies 60^{ \circ} = y \\ \\ [/tex]
[tex] \underline{\boxed{ \sf\therefore Value\:of \: y\:is\:60^{\circ}}}[/tex]
In line segment AB
[tex]\sf \to\angle AOE + \angle EOB = 180^{\circ}\quad\bigg\lgroup Linear\:Pair\bigg\rgroup \\ [/tex]
[tex]\sf where \small{\begin{cases} \sf\angle AOE = z\\ \sf\angle EOB = y \\ \sf y = {60}^{ \circ} \end{cases}}[/tex]
[tex]\bigstar[/tex] Substituting these values:-
[tex]\sf \implies\angle AOE + \angle EOB = 180^{\circ} \\ \\ [/tex]
[tex]\sf \implies z+y = 180\\ \\ [/tex]
[tex]\sf \implies z+60 = 180\\ \\ [/tex]
[tex]\sf \implies z= 180 - 60 \\ \\ [/tex]
[tex]\sf \implies z= 120^{ \circ} \\ \\ [/tex]
[tex] \underline{\boxed{ \sf\therefore Value\:of \: z\:is\:120^{\circ}}}[/tex]