Question

In an isosceles trapezium ABCD, if AB || CD,
show that ZADC + ZABC = 180°.​

Answer 1

Answer:

Step-by-step explanation:

Since ABCD is isosceles trapezium  

So angle DAB =angle ABC =x (say)

and Angle ADC = angle DCB = y (say)

Sum of all angles of quadrilateral is 360  

So x + x +y + y =360

x+y =180

Angle ADP =  

2

y

​  

 and angle DAP =  

2

x

​  

 (Since DP and AP are angle bisectors)

2

y

​  

+  

2

x

​  

 = 90

In triangle APD  

2

y

​  

+  

2

x

​  

 + angle DPA =180

So angle DPA = 90

 So correact answer is Option C