Question

In the given trapezium ABCD, angle bisectors of <A
and <B meet at O. Find <C and <D.​

Answer 1

Step-by-step explanation:

Given :-

ABCD is a Trapezium and The angle bisectors of A and B meet at O. < BAO = 35° and < ABO = 25°

To find :-

Find <C and <D ?

Solution :-

ABCD is a Trapezium.

The angle bisectors of A and B are OA and OB meet at O.

=> < BAO = <OAD

Given that < BAO = 35°

<OAD = 35°

and < ABO = < OBC

Given that < ABO = 25°

=> < OBC = 25°

Now,

< A = < BAO + <OAD

=> < A = 35°+35°

=> < A = 70°

and

< B = < ABO + < OBC

=> < B = 25°+25°

=> < B = 50°

From the given figure,

AB || CD

We know that

The sum of the angle pair between the parallel lines is 180°

< A + < D = 180° and <B+<C = 180°

=> 70° + <D = 180°

=> <D = 180°-70°

=> < D = 110°

and

<B+<C = 180

=> 50°+< C = 180°

=> <C = 180°-50°

=> < C = 130°

Therefore, <C = 130° and < D = 110°

Answer:-

The measurements of <C and <D are 130° and 110° respectively.

Used formulae:-

→ In a Trapezium , One pair of opposite sides are parallel.

→ In a Trapezium, The sum of the angle pair between the parallel lines is 180°.

→ The angle bisector of an angle divides the given angle into two equal parts .