Question

Construct a quadrilateral EFGH, where EF = 6cm, FG = 5.2 cm, $\angle E=75°$, $\angle F=\frac{2}{3}\angle G$ and $\angle F+\angle G=150°$. Measure the value of $\angle H$.

• A. 125°
• B. 85°
• C. 135°
• D. 115°

Answer 1

The correct option is C 135°

Given,
EF = 6 cm, FG = 5.2 cm, $\angle E=75°$, $\angle F=\frac{2}{3}\angle G$ and $\angle F+\angle G=150°$.

If, $\angle G=x$, then $\angle F=\frac{2}{3}x$
From the given question, $x+\frac{2}{3}x=150°$
$\Rightarrow 3x+2x=450°$
$\Rightarrow 5x=450°$
$\Rightarrow x=\frac{450°}{5}=90°$

So, $\angle G=90°,\angle F=\frac{2}{3}\times 90°=60°$.

Steps of Construction:

1. Draw a line segment EF of length 6cm.
2. Construct 75° at E and 60° at F and extend the lines.
3. Keeping F as the centre, cut an arc of radius 5.2 cm on the extended line from the point F.
4. Mark the intersecting point to be G. From the point G, construct a right angle and extend the line.
5. Mark the intersecting point to be H.

Quadrilateral EFGH is hence constructed.


Now, measure $\angle H$. It will be approximately 135°.