NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 2: Geometry - Problems and Solutions

Question 59

Idea: First recall what "acute" and "obtuse" mean. Then read the picture.

Definitions:

Acute angle: measure is less than a right angle.

( ext{Acute: } m(angle) < 90^circ )

Obtuse angle: measure is more than a right angle but less than a straight angle.

( ext{Obtuse: } 90^circ < m(angle) < 180^circ )

Step 1: Look at point E

Two lines cross at ( E ) and make four small angles around ( E ).

Each of these looks smaller than a right angle.

So they are acute: ( angle AEB, angle BEC, angle CED, angle DEA ).

Step 2: Look at vertices B and D

Inside the quadrilateral, the angles at ( B ) and ( D ) open wider than a right angle.

So they are obtuse: ( angle ABC ) and ( angle CDA ).

Conclusion:

Any four acute around ( E ): ( angle AEB, angle BEC, angle CED, angle DEA ).

Any two obtuse at the corners: ( angle ABC, angle CDA ).