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.