Construct an isosceles triangle whose base is 6 cm and whose vertical angle is 75°.

According to the question, vertical angle is 75°. We know that other two angles will be equal because it is an isosceles triangle and sum of the angles is 180°.


x + x + 75°= 180°


2x = 180°- 75°


2x = 105° x = 52.5°


Steps of Construction


1. Draw a line segment AB= 6 cm.



2. Draw A and B = 52.5° such that 105° = 90° + 15° where 15° is the bisector of 30°


and



3. Extend them such that they intersect at C.



6