Question

find the angle between the straight lines 2x+3y=13 and 2x-5y+7=0​

Answer 1

Answer:

There are two angles when the two lines intersect.

34.5°, and 55.5°

Answer 2

Answer:

55.5° and 124.5°

Step-by-step explanation:

2x + 3y = 13 ⇒ y = - $\frac{2}{3}$ x + $\frac{13}{3}$ ; $m_{1}$ = - $\frac{2}{3}$ ⇒ tan β = $\frac{2}{3}$ ⇒ β ≈ 33.69°

2x - 5y + 7 = 0 ⇒ y = $\frac{2}{5}$ x + $\frac{7}{5}$ ; $m_{2}$ = $\frac{2}{5}$ ⇒ tan α = $\frac{2}{5}$ ⇒ α ≈ 21.8°

The angles between the straight lines are 55.5° and 124.5°