Question

$△$XYZ is constructed such that XY = 5 cm, XZ = 8.5 cm and $\angle$X = 75${}^{\circ }$. Then $△$XYZ is

• A. an obtuse scalene triangle
• B. an acute isosceles triangle
• C. a right scalene triangle
• D. an acute scalene triangle

Answer 1

The correct option is D

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 $\angle$Y is 34${}^{\circ }$, measure of $\angle$Z is 71${}^{\circ }$ and the length of side YZ is 8.7 cm.

Hence, the given triangle is an acute-angled scalene triangle.