Question

In Fig. 9.42, AB and CD are two lines intersecting at O. If angleAOC= 35° and angleCOE = 30°, find the values of x, y and z.​

Answer 1

Step-by-step explanation:

Hope this helps u.....

I did this prblm with the concept of linear pair...which means the angle of a line is 180⁰...

x=145⁰

y=115⁰

z=35⁰

Incase of steps required...refer the attachment......

Answer 2

$\underline{\boxed{\bold{Question}}}$  

↠ In Fig. 9.42, AB and CD are two lines intersecting at O. If ∠AOC= 35° and ∠COE = 30°, find the values of x, y and z.​

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$\underline{\boxed{\bold{Important\;Information}}}$  

↠ Vertically opposite angles are angles formed by 2 straight line which are exactly opposite and they are equal.

↠ Sum of linear pair of angles = 180°

↠ Refer attachment for clear figure.

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$\underline{\boxed{\bold{Given}}}$

↠ ∠AOC= 35°

↠∠COE = 30°

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$\underline{\boxed{\bold{Answer}}}$

Let's Start !

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✰ As sum of angles formed on straight line = 180° (Linear Pair)

$:\implies \angle AOC + \angle DOA = 180^{\circ}$

$:\implies 35^{\circ} + x = 180^{\circ}$

$:\implies x = 180^{\circ} - 35^{\circ}$

$\boxed{\red{ :\implies x = 145^{\circ} } }$

✰ As by vertically opposite angles

$:\implies \angle DOA = \angle COE + \angle EOB$

$:\implies 145^{\circ} = 30^{\circ} + y$

$:\implies y = 145^{\circ} - 30^{\circ}$

$\boxed{ \red{:\implies y = 115^{\circ} } }$

✰ As by vertically opposite angles

$:\implies \angle BOD = \angle AOC$

$:\implies z = 35^{\circ}$

$\boxed{ \red{:\implies z = 35^{\circ} } }$

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$\underline{\boxed{\bold{\bigstar \; Verification \; \bigstar}}}$

Sum of all angle formed in circular loop is 360°

$:\implies \angle BOD + \angle BOE + \angle EOC + \angle COA + \angle AOD = 360^{\circ}$

$:\implies z + y + 30^{\circ} + 35^{\circ} + x = 360^{\circ}$

$:\implies 35^{\circ} + 115^{\circ} + 30^{\circ} + 35^{\circ} + 145^{\circ} = 360^{\circ}$

$:\implies 360^{\circ} = 360^{\circ}$

$\boxed {\bold{\blue{LHS = RHS} } }$

Hence Verified.

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$\boxed{\boxed{\bold{\therefore Measure \; of \; \angle x = 145^{\circ}}}}$

$\boxed{\boxed{\bold{\therefore Measure \; of \; \angle y = 115^{\circ}}}}$

$\boxed{\boxed{\bold{\therefore Measure \; of \; \angle z = 35^{\circ}}}}$

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Hope this helps u.../

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