Question

in the adjoining figure the parallel lines m and n are interesected by a transversal line l and angle angle 2 equals to 4 ratio 5 find the measure of all angles from angle 1 to angle 8​

Answer 1

Angle 1: Angle 2 :: 4:5

let the common ratio be x

So angle 1 is 4x and angle 2 is 5x

By linear pair of angle property, angle 1+ angle 2= 180°

or, 4x+5x=180°

or, 9x=180°

or, x= 20

so angle 1= 4x= 80

And angle 2= 5x= 100

So by the properties of vertically opposite angles and alternate interior angles-

∠1 = 80°

∠2= 100°

∠3= ∠1= 80° (vertically opposite)

∠4= ∠2= 100° (vertically opposite)

∠5= ∠4= 100° (alternate interior)

∠6= ∠3= 80° (alternate interior)

∠7=∠5= 100° (vertically opposite)

∠8=∠6= 80° (vertically opposite)

answered.