Question

Draw an angle ABC of measure ${45}^o$, Using ruler and compasses. Now draw an angle DBA of measure ${30}^o$ using ruler and compasses as shown in fig 9.23.
What is the measure of $\angle DBC$

Answer 1

Construct $\angle ABC={45}^o$

• Draw a line I and mark a point B on it. With suitable radius and considering B as centre draw an arc intersecting the line I at P.
• Now, with the same radius and centre P make an arc intersecting the previous arc at a point say X.

• With the same radius take X as centre draw another arc such that it intersects the arc at a point Y.
• With centre X and radius more than half of XY and draw an arc

Construct $\angle ABC={45}^o$

• Now considering Y as centre and draw an arc such that it intersects the previous arc at point 'Z'.
• Join ZB.
• BZ is required perpendicular to line I, i,e,$\angle ZBP={90}^o$

• Take the radius more than half of PQ and centre as P and Q draw arcs and name their intersection as A.
• Join A B
• Thus $\angle ABC={45}^o$

Construct $\angle ABD={30}^o$

Measure the angle $\angle DBC={75}^o$