[4 marks sum]

Question 14 Marks

In the case given below, find the value of x so that POQ is straight line

Answer

POQ is a straight line.
In the given figure,
∵ POQ is a straight line
∴ ∠POL + ∠LOM + ∠MOQ = 180° (Straight line angles)
⇒ x + 20° + 2x - 30° + 3x - 50°= 180°
⇒ 6x + 20° - 80° = 180°
⇒ 6x - 60° = 180°
⇒ 6x = 180° + 60° = 240°
$\Rightarrow x=\frac{240^{\circ}}{6}$
⇒ x = 40°
∴ x = 40°

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Question 24 Marks

Draw a line segment AB = 6 cm. Without using set squares, draw angle OAB = 60° and angle OBA = 90°. Measure angle AOB and write this measurement.

Answer

Steps of construction:

Draw a line segment AB = 6 cm
At A, draw a ray making an angle of 60° with the help of a compass.
At B, draw another ray making an angle of 90° which meet each other at O.
Now on measuring ∠AOB, it is 30°