Question 120

If a straight line L makes an angle θ (θ > 90°) with the positive direction of x axis, then the acute angle made by a straight line L 1 , perpendicular to L, with the yaxis is

Solution

Here, $$L \perp L_1$$ => $$\angle$$OCA = $$\frac{\pi}{2}$$

$$\angle$$CAO = $$\pi - \theta$$

In $$\triangle$$OAC

=> $$\angle$$CAO + $$\angle$$OCA + $$\angle$$COA = $$\pi$$

=> $$\angle$$COA = $$\pi - \frac{\pi}{2} - (\pi - \theta)$$

= $$\theta - \frac{\pi}{2}$$

$$\therefore$$ $$\angle$$BOC = $$\frac{\pi}{2} - (\theta - \frac{\pi}{2})$$

= $$\pi - \theta$$

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If a straight line L makes an angle θ (θ > 90°) with the positive direction of x­ axis, then the acute angle made by a straight line L 1 , perpendicular to L, with the y­axis is