Construction of a Quadrilateral When Two Adjacent Sides and Three Angles Are Given
Construct a q...
Question
Construct a quadrilateral EFGH, where EF = 6cm, FG = 5.2 cm, ∠E=75°, ∠F=23∠G and ∠F+∠G=150°. Measure the value of ∠H.
A
135°
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
115°
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
125°
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
85°
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is A 135° Given,
EF = 6 cm, FG = 5.2 cm, ∠E=75°, ∠F=23∠G and ∠F+∠G=150°.
If, ∠G=x, then ∠F=23x
From the given question, x+23x=150° ⇒3x+2x=450° ⇒5x=450° ⇒x=450°5=90°
So, ∠G=90°,∠F=23×90°=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.