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Angles in Alternate Segments

Two circles i...

Question

$T w o c i r c l e s i n t e r s e c t i n A a n d B . Q u a d r i l a t e r a l s P C B A a n d A B D E a r e i n s c r i b e d i n t h e s e c i r c l e s s u c h t h a t P A E a n d C B D a r e l i n e s e g m e n t s . ∠ P = 95^{0} a n d ∠ C = 40^{0} . F i n d t h e v a l u e o f Z .$

A

85⁰

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B

75⁰

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C

105⁰

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D

None of these

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Solution

The correct option is A
85⁰

In PABC,

$∠ P + ∠ B = 180^{\circ}$

$\Rightarrow ∠ B = 180^{\circ} - 95^{\circ} = 85^{\circ}$

$∠ C B D = 180^{\circ}$ ( Linear pair)

So, $∠ D B A = 180^{\circ} - 85^{\circ} = 95^{\circ}$

In ABDE,

$∠ B + ∠ E = 180^{\circ} \Rightarrow ∠ E = Z^{\circ}$

$Z^{\circ} = 180^{\circ} - 95^{\circ} = 85^{\circ}$

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