△XYZ is constructed such that XY = 5 cm, XZ = 8.5 cm and ∠X = 75∘. Then △XYZ is
an acute scalene triangle
Step 1:
Draw the base line XY of the length 5 cm.
Step 2:
Measure the angle X with your protractor. Make a mark at 75 degrees and draw a line from X passing through the mark.
Step 3:
Cut an arc of radius 8.5 cm on the line passing through the point X. The point where this arc cuts the line is the point Z.
Step 4:
Draw a line from Y to point Z, to get the required triangle XYZ, as shown below.
From the above construction, we see that the measure of ∠Y is 34∘, measure of ∠Z is 71∘ and the length of side YZ is 8.7 cm.
Hence, the given triangle is an acute-angled scalene triangle.