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ICSE Class 10 Answered

Find x and y          Angle ADC
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Asked by ayush421301 | 06 Jan, 2020, 02:21: PM
answered-by-expert Expert Answer
In the figure, angle ABP = 30o. ABCD is a cyclic quadrilateral.
We need to find the value of x and y if x=2y and also need to find measure of angle ADC.
angle A B P equals 30 degree rightwards double arrow angle C B Q equals 30 degree space... left parenthesis i right parenthesis space left parenthesis V e r t i c a l l y space o p p o s i t e space t o space angle A B P right parenthesis P comma space B comma space C space a r e space i n a space s t r a i g h t space l i n e space rightwards double arrow space angle P B C space i s space a space s t r a i g h t space a n g l e rightwards double arrow angle A B C equals 180 degree minus angle A B P equals 150 degree Q u a d r i l a t e r a l space A B C D space i s space a space c y c l i c space q u a d r i l a t e r a l rightwards double arrow angle A B C space a n d space angle A D C space a r e space s u p p l e m e n t a r y space a n g l e s rightwards double arrow angle A B C space plus space angle A D C space equals space 180 degree rightwards double arrow space angle A D C space equals space 30 degree space.... space left parenthesis i i right parenthesis A l s o comma space angle B A D space a n d space angle B C D space a r e space s u p p l e m e n t a r y space a n g l e s rightwards double arrow angle B A D plus space angle B C D space equals space 180 degree space... space left parenthesis i i i right parenthesis angle B A D space i s space a n space e x t e r i o r space a n g l e space o f space triangle A B P space a n d space s u p p l e m e n t a r y space w i t h space angle P A B rightwards double arrow angle B A D equals angle A P B plus angle A B P equals x plus 30 degree space... space left parenthesis i v right parenthesis angle B C D space i s space a n space e x t e r i o r space a n g l e space o f space triangle B C Q space a n d space s u p p l e m e n t a r y space w i t h space angle B C Q rightwards double arrow angle B C Q equals angle C B Q plus angle B Q C equals y plus 30 degree space.... space left parenthesis v right parenthesis F r o m space left parenthesis i i i right parenthesis comma space left parenthesis i v right parenthesis space a n d space left parenthesis v right parenthesis comma space w e space h a v e x plus 30 degree plus y plus 30 degree equals 180 degree space rightwards double arrow 2 y plus 30 degree plus y plus 30 degree equals 180 degree space rightwards double arrow 3 y plus 60 degree equals 180 degree rightwards double arrow y plus 20 degree equals 60 degree rightwards double arrow y equals 40 degree rightwards double arrow x equals 80 degree
Answered by Renu Varma | 07 Jan, 2020, 11:07: AM

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