Question

Construct a ΔXYZ with YZ = 7.5 cm, ∠Y = 60° and ∠Z = 45°. Draw the bisectors of ∠Y and ∠Z. If these bisectors meet at O, measure angle YOZ.

Answer 1

Steps of construction:
1. Draw a line segment YZ = 7.5 cm.
2. With Y as centre, draw an arc cutting YZ at L.
3. With L as centre and same radius, cut the arc at M.
4. Join Y and M. Produce YM to S. YS makes an angle of 60° with YZ.
5. With Z as centre, draw an arc cutting YZ at P.
6. With P as centre and same radius, cut the arc at Q, and with Q as centre and same radius cut the arc at R. Using Q and R, Draw UZ perpendicular to YZ.
7. Bisect ∠UZY. Let TZ be the bisector. TZ makes an angle of 45° with YZ.
8. Bisect ∠SYZ and ∠TZY.
9. Mark the point as O where the bisectors of ∠SYZ and ∠TZY meet.
10. On measuring ∠YOZ = 127.5°.