Q17 of 24 Page 16

In a quadrilateral ABCD, CO and DO are the bisectors of ∠C and ∠D respectively. Prove that ∠COD = (∠A +∠B).

Sum of angles of a quadrilateral is 360°


In the quadrilateral ABCD



∠A + ∠B + ∠C + ∠D = 360°


∠A + ∠B =



…….(i)


Now in Δ DOC


[Sum of angles of a triangle is 180°]



……….(ii)


From above equations (i) and (ii) RHS is equal therefore LHS will also be equal.


Therefore


More from this chapter

All 24 →
15

In Fig. 16.21, the bisectors of ∠A and ∠B meet at a point P. If ∠C =100° and ∠D = 50°, find the measure of ∠APB.

 16

In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1 : 2 : 4 : 5. Find the measure of each angle of the quadrilateral.

 18

Find the number of sides of a regular polygon, when each of its angles has a measure of

(i) 160°


(ii) 135°


(iii) 175°


(iv) 162°


(v) 150°

 19

Find the numbers of degrees in each exterior angle of a regular pentagon.