Question

The obtuse angle between the lines y = -2 and y = x +2 is __ (degree)

Answer 1

We can compare the given lines with y=mx+c {where m is the slope of the line}
Slope of the line $y=-2,m_1=0$
Slope of the line $y=x+2,m_2=1$
Acute angle between these two lines
$tan\theta =|\frac{m_1-m_2}{1+m_1.m_2}|$
$=|\frac{0-1}{1}|$
$tan\theta =1$
$\theta ={45}^o$
Hence obtuse angle between the lines = ${180}^o-{45}^o$
$={135}^o$