## Construct a triangle XYZ in which ∠Y = 30°,

[question] Question. Construct a triangle $X Y Z$ in which $\angle Y=30^{\circ}, \angle Z=90^{\circ}$ and $X Y+Y Z+Z X=11 \mathrm{~cm}$. [/question] [solution] Solution: The below given steps will be followed to construct the required triangle. Step I: Draw a line segment AB of 11 cm. (As $X Y+Y Z+Z X=11 \mathrm{~cm}$ ) Step II: Construct an angle, ∠PAB, of 30° at point A and an angle, ∠QBA, of 90° at point B. Step III: Bisect ∠PAB and ∠QBA. Let these bisectors intersect each other at point X. S...

## construct an angle of 45° at the initial point of a given

[question] Question. Construct an angle of 45° at the initial point of a given ray and justify the construction. [/question] [solution] Solution: The below given steps will be followed to construct an angle of 45°. (i) Take the given ray PQ. Draw an arc of some radius taking point P as its centre, which intersects PQ at R. (ii) Taking R as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at S. (iii) Taking S as centre and with the same radius as before...

## Construct an angle of 90° at the initial point of a given ray and justify the construction.

[question] Question. Construct an angle of 90° at the initial point of a given ray and justify the construction. [/question] [solution] Solution: The below given steps will be followed to construct an angle of 90°. (i) Take the given ray PQ. Draw an arc of some radius taking point P as its centre, which intersects PQ at R. (ii) Taking R as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at S. (iii) Taking S as centre and with the same radius as before...