Question

The diagram shows the construction of a parallelogram KLMN. The width of the compasses for step I and step II are the same. LKLM = .......... .

• A. ${45}^{\circ }$
• B. ${60}^{\circ }$
• C. ${120}^{\circ }$
• D. ${135}^{\circ }$

Answer 1

The correct option is C ${120}^{\circ }$

Given the width of the compass for step I and step II are the same.

After having cut an arc with a certain width at K, we cut another arc of the same width keeping the compass at I.

Draw a line passing through K. This measures 60 deg.

We know that KLMN is a parallelogram and that its adjacent angles are supplementary.

So, angle KLM is 120 deg.