Three angles of a quadrilateral are equal,fourth angle is right angle . Find the measures of the angles.Classify the quadrilateral as convex, concave, trapezium etc.

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Solution

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$L e t t h e a n g l e o f a q u a d r i l a t e r a l b e x . B y a n g l e s u m p r o p e r t y o f q u a d r i l a t e r a l x + x + x + 90 ° = 360 ° [S i n c e i t i s g i v e n t h a t t h r e e a n g l e s o f a q u a d r i l a t e r a l a r e e q u a l a n d f o u r t h a n g l e i s 90 °] \Rightarrow 3 x = 270 ° \Rightarrow x = 90 ° S o, a l l a n g l e s o f a q u a d r i l a t e r a l m e a s u r e s 90 ° . I t i s e i t h e r a s q u a r e o r a r e c \tan g l e b e c a u s e i n s q u a r e a n d r e c \tan g l e a l l f o u r a n g l e s m e a s u r e 90 ° . I t i s a c o n v e x q u a d r i l a t e r a l b e c a u s e n e i t h e r o f t h e f o u r a n g l e i s e x c e e d i n g 180 ° .$
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