Question

Angle between straight lines y+4=xtan10deqree and y+4=xtan40dgree

Answer 1

Answer:

30°

Step-by-step explanation:

To find ---> Angle between straight lines

y + 4 = x tan10°

y + 4 = x tan40°

Solution--->

We know that slope intercept form of equation is

y = mx + c

Where m is slope of line and c is length of intercept cut by line on y axis.

If θ is the angle made by line with positive x axis then

m = tanθ

Now returning to original problem

y + 4 = x tan10°

y = x tan10° - 4 ................... (1)

Comparing equation (1) with y = m₁x + c₁

m₁ = tan10° , c₁ = -4

y + 4 = x tan40°

y = x tan40° - 4 .....................(2)

Cpmparing equation (2) with y = m₂x + c₂

m₂ = tan40° , c₂ = -4

Let angles made by line (1) and line(2) with positive x axis be θ₁ and θ₂ respectively.

So

Slope of line (1) = tanθ₁

m₁ = tanθ₁

tan10° = tanθ₁

10° = θ₁

θ₁ = 10°

Slope of line(2) = tanθ₂

m₂ = tanθ₂

tan40° = tanθ₂

40° = θ₂

θ₂ = 40°

∠PAX= 40° , ∠ QBX= 10°

∠ OAB= 180° - ∠ PAX (linear pair of ∠ )

= 180° - 40° = 140°

∠ OBA =∠QBX =10°(vertically opposite∠)

In Δ OAB by anglesum property

∠AOB + ∠OAB + ∠OBA = 180°

∠AOB + 140° + 10° = 180°

∠ AOB = 180° - 150°

∠AOB = 30°

Angle between two lines = 30°

Answer 2

$<font color =“orange”>$

$\huge\red{\boxed{\bold{ANSWER}}}$

30°

#answerwithquality #bal

$<marquee scrollamount=500>follow me </marquee>$