using a ruler and a pair of compasses; construct a triangle xyz such that /xy/= 10cm, zxy= 120 degree and xyz=30degree

it is easy to construct an equilateral triangle, giving you a 60° angle.

Now you can double that and halve that for the two angles you want.

That should get you started.

To construct the triangle XYZ using a ruler and a pair of compasses, follow these steps:

1. Begin by drawing a straight line segment XY of a length 10 cm using your ruler. Label the endpoints as X and Y.

2. Place the center of your compass at point X and draw an arc with any radius greater than half the length of XY. This arc should intersect line XY. Label this point of intersection as Z.

3. Without changing the radius, place the center of your compass at point Z and draw an arc that intersects the first arc previously drawn. Label the point of intersection with the first arc as A.

4. Using your ruler, draw a line segment XA.

5. Bisect the angle ZXY by drawing an arc from both X and Y that intersects at some point B. To bisect an angle, place the center of your compass at X, adjust the compass width to a convenient width, and draw an arc that intersects line XY. Repeat this step with the center of your compass at Y, drawing another arc that intersects line XY.

6. Use your ruler to draw a straight line segment from point Z to point B.

7. Finally, label the angles X, Y, and Z as angle XYZ, angle YXZ, and angle ZXY respectively.

By following these steps, you should have successfully constructed triangle XYZ with the given properties.