Question

Construct a triangle using the given data: PQ = 6.2cm, ∠P = 105° and ∠ = 45°

Answer 1

PQ = 6.2cm, ∠P = 105° and ∠ = 45°

Steps of Construction:
1. Draw a line segment PQ = 6.2cm.
2. With P as centre, draw an arc meeting PQ at A.
3. With A as centre and same radius, cut the arc at B and with BQ as centre and same radius, cut the arc at C.
4. With B and C as centre, cut arcs and draw PM perpendicular to PQ.
5. Bisect ∠MPC. Let PX be the bisector. PX makes an angle of 105° with PQ.
6. With Q as centre, draw an arc meeting PQ at S.
7. With S as centre and same radius, cut the arc at T and with T as centre and same radius, cut the arc at U.
8. With T and U as centre, cut arcs and draw QN perpendicular to PQ.
9. Bisect  ∠NQP. Let QY be the bisector. QY makes an angle of 45° with PQ.
10. Mark the point as R, where PX and QY cut each other.
Thus, PQR is the required triangle.