Question

Draw an angle ABC of measure 45°, using ruler and compasses. Now draw an angle DBA of measure 30o , using ruler and compasses as shown in figure. What is the measure of ∠DBC?

Answer 1

Steps of construction:

(i) Draw a ray `vec(BC)`

(ii) With B as centre and any radius draw an arc which cuts BC at P.

(iii) With centre P and same radius, draw an arc which cuts the previously drawn arc at Q.

(iv) Similarly, with Q as centre and same radius draw an another arc which cuts the previously drawn arc at R.

(v) With centre R and Q and same radius draw the arcs which cuts each other at S.

(vi) Join BS which cuts the arc RP at T.

(vii) With centre P and T and radius more than `1/2 (hat(PT))` draw the arcs which cuts each other at U.

(viii) Join BU and produce it to a point A. Thus ∠ABC = 45°.

(ix) Now, with B as centre draw another arc which cuts the line AB at X.

(x) With centre X and same radius draw an arc which cut the arc drawn in step (ix) at Y.

(xi) With centre X and Y and radius more than `1/2 (hat(XY))` draw two arcs which cuts each other at Z.

(xii) Join BZ and produced it to a point D. Thus ∠ABD = 30°. On measuring, we get ∠DBC = 75°.