1 Marks Question

Question 11 Mark

In the figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that $\angle ROS={1\over2}(\angle QOS-\angle POS)$

Answer

Ray OR is perpendicular to line PQ
$\therefore$ $\angle$QOR = $\angle$POR = 90^o . . . .(1)
$\angle$QOS = $\angle$QOR + $\angle$ROS. . . .(2)
$\angle$POS = $\angle$POR – $\angle$ROS. . . .(3)
From (2) and (3),
$\therefore$ $\angle$QOS – $\angle$POS = ($\angle$QOR – $\angle$POR) + 2$\angle$ROS = 2$\angle$ROS . . . [Using (1)]
$\therefore$ $\angle ROS={1\over2}(\angle QOS-\angle POS)$

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Question 21 Mark

In figure, if x + y = w + z, then prove that AOB is a line.

Answer

Given that, x + y = w + z ... (1)
As the sum of all angles round a point is equal to 360^o
$\therefore$ x + y + w + z = 360^o
$\therefore$ x + y + x + y = 360^o
$\therefore$ 2(x + y) = 360^o
$\therefore$ $x+y={360^0\over2}$
$\therefore$ x + y = 180^o
$\therefore$ AOB is a line.

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Question 31 Mark

An angle is five times its complementary angle. Find the measure of the angle.

Answer

$75^{\circ}$

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Question 41 Mark

If two lines intersect at a point then how many pair of adjacent angles are there?

Answer

Four

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Question 51 Mark