Construct a triangle XYZ whose perimeter 15 cm and whose base angles are 60° and 70°.

Here, we have been given the perimeter and base angles of the triangle.

Steps of construction are:

1. Draw a line segment using a ruler; locate points P and Q such that PQ = 15 cm.

2. Construct rays PR such that ∠QPR = 60° and QS such that ∠PQS = 70° using compass and then measure it with protractor.

3. Draw the bisectors PL and QM of ∠QPR and ∠PQS respectively. Let it intersect it at X.

4. Draw the perpendicular bisector of XP and XQ and let these intersect PQ at Y and Z respectively.

In order to draw perpendicular bisector of XP, fix one end of the compass at P at more than half of the length of XP and make a complete circle or arcs on both sides of line XP, and the other end of compass at X and intersect with the previous arcs. Do similar with the line segment XQ. Here, we’ve made complete circles.

5. Join XY and XZ.

Thus, XYZ is the required triangle.