Q. 115.0( 2 Votes )

The bisectors of two adjacent angles of a parallelogram intersect at
A. 30°

B. 45°

C. 60°

D. 90°

Answer :


Let ABCD is a parallelogram.


The angle bisectors AE and BE of adjacent angles A and B meet at E.


AD || BC (Opposite sides of ||gm)


DAB + CBA = 180°


2EAB + 2EBA = 180° (sum of the interior angles, formed on the same side of the transversal, is 180°)


AE and BE are the bisectors of DAB and CBA respectively.


EAB + EBA = 90° ... (1)


In ∆EAB,


EAB + EBA + AEB = 180° (sum of the angles of a triangle is 180°)


90° + AEB = 180°


From (1)


AEB = 90°

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
Members of QuadrilateralsMembers of QuadrilateralsMembers of Quadrilaterals65 mins
Genius Quiz | Understanding QuadrilateralsGenius Quiz | Understanding QuadrilateralsGenius Quiz | Understanding Quadrilaterals20 mins
Quiz | Polygon & their PropertiesQuiz | Polygon & their PropertiesQuiz | Polygon & their Properties46 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
NCERT | Standard Form of NumbersNCERT | Standard Form of NumbersNCERT | Standard Form of Numbers41 mins
Metals of SurprisesMetals of SurprisesMetals of Surprises38 mins
Quiz on Mystery of OnionQuiz on Mystery of OnionQuiz on Mystery of Onion30 mins
Champ Quiz | Spelling of important wordsChamp Quiz | Spelling of important wordsChamp Quiz | Spelling of important words47 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