Construct a

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 = 12 cm.

2. Construct rays PR such that ∠QPR = 65° and QS such that ∠PQS = 85° 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 A.

4. Draw the perpendicular bisector of AP and AQ and let these intersect PQ at B and C respectively.

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

5. Join AB and AC.

Thus, ABC is the required triangle.