Question

The acute angle between the lines $x-y=0$ and $y=0$ is

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

Given

$x-y=0$

$y=0$ represents $x-axis$

So the slope of line $x-y=0$ is $-\frac{1}{-1}=1$

$⟹\tan \theta =1$

$\tan \theta =\tan \frac{\pi }{4}$

$\theta =\frac{\pi }{4}$

$\theta ={45}^{\circ }$