Question

How many of the following statements are correct?

If AB and OC are straight lines and the angle made by OC with OB is ${30}^o$, then $\theta ={150}^o$

(2)

The angle made by OA with respect to positive x-axis is ${120}^{o}or-{240}^o$.

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Answer 1

(1) $\theta$ and ${30}^o$ are supplementary angles or $\theta +{30}^o={180}^o$

$\Rightarrow \theta =150$

If we measure the angle in anticlockwise direction, we get ${90}^o+{30}^o={120}^o$.

When we measure the angle in clockwise direction, we get $-({180}^o+{60}^o)=-{240}^o$ we can see here that the difference of these angles is ${360}^o({120}^o-(-{240}^o\left)\right)$
Key steps: (1) clockwise and anticlockwise way of measuring angles
(2) Concept of supplementary angles