Question

Construct the circumcircle of $△$KLM in which LM=7 cm, $\angle$K = 60$°$ and $\angle$M = 55$°$.

Answer 1

$$\begin{gathered} \angle \mathrm{K}+\angle \mathrm{L}+\angle \mathrm{M}=180°(\mathrm{Angle}\mathrm{sum}\mathrm{property}) \\ \Rightarrow \angle \mathrm{L}=180°-\angle \mathrm{K}-\angle \mathrm{M} \\ \Rightarrow \angle \mathrm{L}=180°-60°-55°=65° \end{gathered}$$
Steps of construction:
1. Draw a line segment LM = 7 cm.
2. Draw $\angle \mathrm{MLY}=65°$.
3. Draw another angle $\angle \mathrm{LMX}=55°$. The rays LY and MX intersect at point K.
4. Then $∆$KLM is the required triangle.
5. Draw perpendicular bisectors of sides KL and LM (any two sides) which intersect at O.
6. Taking OK or OL or OM as the radius, draw the required circumcircle.