MATHS M.C.Q. [1 Marks Each]

 From the given figure it is clear that,
$2a + 5b = 180^\circ [$Liner pair$]$
$\Rightarrow 2 \times 40^\circ + 5b$ $180^\circ [\because a = 40^\circ ]$
$\Rightarrow 80^\circ + 5b = 180^\circ $
$\Rightarrow 5b = 180^\circ - 80^\circ $
$\Rightarrow 5b = 100^\circ $
$\Rightarrow\text{b}=\frac{100^\circ}{5}$
$\Rightarrow b = 20^\circ $

 Let one angle be $x$ then the other be $2x.$
Then according to the problem we have, $2x + x = 180^\circ [$ Since two angles are said to be supplementary if their sum is $180^\circ $ or, $3x = 180^\circ $ or, $x = 60^\circ .$
So the measure of the angle is $60^\circ .$

 Let the angles be $2x$ and $3x$
Now, $2x + 3x = 90^\circ $
$\Rightarrow 5x = 90^\circ $
$\Rightarrow x = 18^\circ $
$\therefore$ Larger angle $= 3x = 3 \times 18^\circ = 54^\circ $
Hence, the correct answer is option $(b).$

Since, $PQ || RS$
$\therefore \angle \text{PAC}= \angle \text{ACS}=100^\circ$ [Corresponding angles]
Now, $\angle \text{PAC}=100^\circ$
$\Rightarrow \angle \text{PAB}+\angle \text{BAC}=100^\circ$
$\Rightarrow 60^\circ+\angle \text{BAC}=100^\circ$
$\Rightarrow \angle \text{BAC}=40^\circ$
Hence, the correct answer is option $(a).$

Let the required angle be $\theta $
$\therefore$ supplementary angle $= 180 - \theta $
$\therefore \theta = 4 \times (180 - \theta )$
$\Rightarrow 5\theta = 720$
$\therefore \theta = 144$

$1$ turn $= 4$ right angles
$\therefore 4 $turns $= 4 \times 4 = 16$ right angles and$  \frac{1}{2}​$ turn $= 2$ right angles.
So, the number of right angles in four and half turns $= 16 + 2 = 18$