Question

Find the value of z , y , z in the diagram .
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Answer 1

Step-by-step explanation:

this is your answer in the above picture.

Answer 2

Given:

• ∠AOE = z
• ∠EOB = y
• ∠BOD = x
• ∠DOC = 90°
• ∠COA = 2x

Find:

• Value of x, y and z

Solution:-

In line segment AB

$\sf \to\angle AOC +\angle DOC + \angle DOB = 180^{\circ}\quad\bigg\lgroup Linear\:Pair\bigg\rgroup$

$\sf where \small{\begin{cases} \sf\angle AOC = 2x \\ \sf\angle DOC = {90}^{ \circ} \\ \sf\angle DOB = x\end{cases}}$

$\bigstar$ Substituting these values:-

$\sf \implies\angle AOC +\angle DOC + \angle DOB = 180^{\circ}$

$\sf \implies 2x +90+ x = 180$

$\sf \implies 3x +90 = 180$

$\sf \implies 3x= 180 - 90$

$\sf \implies 3x=90$

$\sf \implies x= \dfrac{90}{3}$

$\sf \implies x= {30}^{ \circ}$

$\underline{\boxed{ \sf\therefore Value\:of\:x\:is\:30^{\circ}}}$

Now,

$\sf \to \angle AOC = \angle EOB\quad\bigg\lgroup Vertical\:Opposite\: Angles\bigg\rgroup$

$\sf where \small{\begin{cases} \sf\angle AOC =2x \\ \sf \angle EOB = y \\ \sf x = {30}^{ \circ} \end{cases}}$

$\bigstar$ Substituting these values:-

$\sf \implies\angle AOC = \angle EOB$

$\sf \implies 2x = y$

$\sf \implies 2(30) = y$

$\sf \implies 60^{ \circ} = y$

$\underline{\boxed{ \sf\therefore Value\:of \: y\:is\:60^{\circ}}}$

In line segment AB

$\sf \to\angle AOE + \angle EOB = 180^{\circ}\quad\bigg\lgroup Linear\:Pair\bigg\rgroup$

$\sf where \small{\begin{cases} \sf\angle AOE = z\\ \sf\angle EOB = y \\ \sf y = {60}^{ \circ} \end{cases}}$

$\bigstar$ Substituting these values:-

$\sf \implies\angle AOE + \angle EOB = 180^{\circ}$

$\sf \implies z+y = 180$

$\sf \implies z+60 = 180$

$\sf \implies z= 180 - 60$

$\sf \implies z= 120^{ \circ}$

$\underline{\boxed{ \sf\therefore Value\:of \: z\:is\:120^{\circ}}}$