Question

Construct $△XYZ$ in which $\angle Y={30}^o,\angle Z={60}^o$ and $XY+YZ+ZX=10$ cm.

Answer 1

Steps for construction :

Step 1: Draw a line segment $QR=10.5$ cm.

Step 2: From point $Q$ draw a ray $QD$ at ${30}^{\circ }$ and from $R$ draw a ray $RE$ at ${60}^{\circ }$.

Step 3: Draw angle bisectors of $\angle Q$ and $\angle R$ such that they intersect each other at point $X$.

Step 4: Draw a line bisector of $QX$ and $XR$ such that these line bisectors intersect $QR$ at point $Y$ and $Z$ respectively.

Step 5: Join $XY$ and $XZ$.

Hence, $△XYZ$ is the required triangle.