Q. 44.2( 24 Votes )

In the adjoining figure, ABCD is a quadrilateral such that D + C = 100°. The bisectors of A and B meet at P. Determine APB.


Answer :

We know that the sum of the angles in a quadrilateral is 3600.


i.e, A + B + C + D = 3600. ...... (1)


We also know that the sum of angles in a triangle is 1800.


According to the problem, it is given that C + D = 1000.


Substituting the condition in the eq(1) we get,


A + B + 1000 = 3600


A + B = 3600 - 1000


A + B = 2600.



. ...... (2)


According to the problem, it is given that the ΔABP is formed by the intersection of angular bisectors of A and B.


From ΔABP, We can write that,



1300 + P = 1800 (From eq(2))


P = 1800 - 1300


P = 500.


The value of the P is 500.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
QuadrilateralsQuadrilateralsQuadrilaterals32 mins
Smart Revision | Let's Revise Properties of PolygonSmart Revision | Let's Revise Properties of PolygonSmart Revision | Let's Revise Properties of Polygon32 mins
Smart Revision | Let's Classify Quadrilaterals and Find their PropertiesSmart Revision | Let's Classify Quadrilaterals and Find their PropertiesSmart Revision | Let's Classify Quadrilaterals and Find their Properties34 mins
NCERT I Quiz on Understanding QuadrilateralsNCERT I Quiz on Understanding QuadrilateralsNCERT I Quiz on Understanding Quadrilaterals54 mins
Genius Quiz | Understanding QuadrilateralsGenius Quiz | Understanding QuadrilateralsGenius Quiz | Understanding Quadrilaterals20 mins
Quiz | Polygon & their PropertiesQuiz | Polygon & their PropertiesQuiz | Polygon & their Properties46 mins
Members of QuadrilateralsMembers of QuadrilateralsMembers of Quadrilaterals65 mins
Smart Revision | All Types of Quadrilaterals and Their PropertiesSmart Revision | All Types of Quadrilaterals and Their PropertiesSmart Revision | All Types of Quadrilaterals and Their Properties35 mins
Champ Quiz | Polygons (Quadrilaterals)Champ Quiz | Polygons (Quadrilaterals)Champ Quiz | Polygons (Quadrilaterals)30 mins
NCERT |  Discussion on Imp. Qs. of  QuadrilateralsNCERT |  Discussion on Imp. Qs. of  QuadrilateralsNCERT | Discussion on Imp. Qs. of Quadrilaterals43 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses