Using ruler and a pair of compasses only
I.construct a triangle ∆XYZ such that XY=10cm angle <YXZ=45° and angle <XYZ=60°
ii.construct the perpendicular bisector of XY and YZ to meet P.
iii.Measure PX
Images can't be sent here. A ruler and compasses should be enough for you. MathWareHouse has some tips on geometric constructions, perhaps you could look there.
KOFI NADEI
To construct the triangle ∆XYZ, follow these steps using a ruler and a pair of compasses:
i. Constructing triangle ∆XYZ:
1. Start by drawing a line segment XY of length 10 cm using a ruler.
2. Place the compass at point Y and draw an arc with any radius that intersects line XY. Label the point where the arc intersects XY as point A.
3. Without changing the compass's radius, place the compass at point A and draw an arc that intersects the previously drawn arc. Label the point of intersection as point Z.
4. Draw a line segment XZ to complete the triangle ∆XYZ.
You have constructed triangle ∆XYZ with XY = 10 cm, angle ∠YXZ = 45°, and angle ∠XYZ = 60°.
ii. Constructing the perpendicular bisectors of XY and YZ:
1. Place the compass at point X and draw an arc that intersects line XY.
2. Without changing the compass's radius, place the compass at point Y and draw another arc that intersects the arc drawn in the previous step.
3. Repeat the above steps to draw an intersecting arc from point Y onto line YZ.
4. Draw a straight line that passes through the intersecting points of these arcs. This line is the perpendicular bisector of XY and YZ.
iii. Measuring PX:
1. Place the compass at point P and draw a circle that intersects the perpendicular bisectors of XY and YZ.
2. Measure the length of the line segment PX using a ruler to determine the distance.
Note: Ensure accuracy while constructing the angles and lines.