Construct an obtuse-angled triangle which has a base of $5.5 c m$ and base angles of $30^{\circ}$ and $120^{\circ}$ .
[5 marks]

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Solution

Let the triangle to be constructed be $Δ A B C$ .
Given:
$B C = 5.5 c m$ , $∠ A B C = 120^{\circ}$ and $∠ A C B = 30^{\circ}$
[1 mark]

Steps of construction:
Step I: Draw a line segment $B C$ of length $5.5 c m$ using ruler.
[0.5 marks]
Step II: Draw an angle of $120^{\circ}$ on point $B$ and produce it to ray $Y$ .
[0.5 marks]
Step III: Draw an angle of $30^{\circ}$ on point $C$ and produce it to ray $X$ .
[0.5 marks]
Step IV: Extend $- - \to B Y$ and $- - \to C X$ to intersect at point $A$ .
[0.5 marks]

Hence, $Δ A B C$ is the required triangle with $B C = 5.5 c m$ , $∠ A B C = 120^{\circ}$ and $∠ A C B = 30^{\circ}$ .
[2 marks]

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Construct an obtuse-angled triangle which has a base of 5.5 cm and base angles of 30∘ and 120∘. [5 marks]

Construct an obtuse-angled triangle which has a base of $5.5 c m$ and base angles of $30^{\circ}$ and $120^{\circ}$ .
[5 marks]