Construct ΔXYZ in which ∠Y =58°, ∠X = 46° and perimeter of triangle is 10.5 cm.

Given: ∠Y =58°, ∠X = 46° and perimeter of Δ PQR

Steps of construction:

i: Draw a line segment QR of 10.5cm.

ii: From point Q draw a ray QD at 58° and from R draw a ray RE at 46°

iii: Draw an angle bisector of Q and R, two angle bisectors intersect each other at point X.

iv: Draw a line bisector of QX and XR respectively these two-line bisectors intersect at point Y and Z

v: Join XY AND XZ.

vi: Δ XYZ is required triangle.