Question

Illustrate the steps of construction to construct a $\angle ABC$ in which $\angle B={75}^{\circ },\angle C={60}^{\circ }$ and AB + BC + AC = 12 cm.

Answer 1

We need to to construct a $\Delta ABC$ in which $\angle B={60}^{\circ },\angle C={45}^{\circ }andAB+BC+AC=12cm.$

The steps to be followed are:-
Step 1: Draw a line segment XY = 12 cm
Step 2: At X, construct an angle of ${75}^{\circ }$ and at y construct an angle of ${60}^{\circ }$
Step 3: Bisect these angles. Let bisector of these angles intersect at point A
Step 4: Draw perpendicular bisector PQ of XA to intersect XY at B and RS of YA to intersect XY at C
Step 5: Join AB and AC to obtain required $\Delta ABC$.
Step 6: $\Delta ABC$ is the required triangle.