Question

Construct a △ ABC in which BC = 4.8cm, ∠B = 45° and ∠C = 75°. Measure ∠A.

Answer 1

Steps of Construction:

Construct a line segment BC = 4.8cm

Considering B as centre and any radius, construct an arc which intersects BC at point P

Considering P as centre and same radius, construct an arc which intersects the previous arc at the point Q

Considering Q as centre and same radius, construct an arc which intersects the arc in step 2 at the point R

Considering R and Q as centres and radius more than half of RQ, construct arcs intersecting each other at the point S

Join BS which intersects the arc in step 2 at the point G so ∠SBC = 90^o

Considering P as centre and radius more than half of PG, construct an arc

Considering G as centre and same radius, construct an arc which intersects the previous arc at the point X

Join B and extend it so ∠B = 45^o

Draw ∠TCB = 90^o

Considering M and H as centres and radius more than half of MH, construct arcs which intersect each other at point Y

Join CY and extend it so ∠C = 75^o

BX and CY intersects at point A after extending

So, △ ABC is the required triangle

Therefore, ∠A = 60^o