Question

Construct a triangle XYZ in which $XY=5cm$ , $YZ=5.5cm$ and $\mathrm{\angle }XYZ={100}^{\circ }$.

Answer 1

Hint: We can draw the base of the triangle of a given length using a ruler. Then we can mark the angle using a protractor. Then we can mark the length of the other side using a compass. Then we can join the points to get the required triangle.

Complete step by step answer:

We need to construct a triangle XYZ with $XY=5cm$ , $YZ=5.5cm$ and $\mathrm{\angle }XYZ={100}^{\circ }$
Firstly, we can draw the base XY. We can draw a line of length $5cm$ using a ruler. Then label the endpoints of the line as X and Y.
It is given that $\mathrm{\angle }XYZ={100}^{\circ }$ . So, we can make an angle of ${100}^{\circ }$ at point Y and extend it using a ruler.
Then we can take a compass and keeping the distance of 5.5cm, we can draw an arc that cuts the line from Y. We can mark the point of intersection of the line and the arc as Z.
Finally, we can join the points X and Z to form a triangle. We can label the triangle with the given length of the sides and measure the angle.

Note: Alternate approach to the problem is,
Firstly, we can draw the base YZ. We can draw a line of length 5.5cm using a ruler. Then label the endpoints of the line as Y and Z.
It is given that $\mathrm{\angle }XYZ={100}^{\circ }$ . So, we can make an angle of ${100}^{\circ }$ at point Y and extend it using a ruler.
Then we can take a compass and draw an arc with a radius of 5 cm that cuts the line from Y. We can mark the point of intersection of the line and the arc as X.
Finally, we can join the points X and Z to form a triangle. We can label the triangle with the given length of the sides and measure the angle.