Question

Construct an isosceles triangle whose base is 6 cm and whose vertical angle 18 75°.

Answer 1

Steps of construction:
1. Draw a line segment BC = 6 cm.
2. Construct $\angle$CBX = 75$°$.
4. Make $\angle$XBY = 90$°$.
5. Draw the right bisector PQ of BC, intersecting BY at O.
6. With O as the centre and radius OB, draw a circle intersecting PQ at A.
7. Join AC and AB.
Thus, ABC is the required triangle.