Question

Please help I hate geometry

Answer 1

m∠1 = 75° m∠2 =45° m∠3 = 60°

Explanation:

m∠1 = 180 - { (180 - 135) + (180 - 120) }

m∠1 = 180 - { 45 + 60 }

m∠1 = 75°

The angle between 1 and 3, lets call it x, is vertically opposite to ∠2, so we must find it first to be able to get ∠2

Since a ║b

Therefore ∠x and ∠135 are co-interior angles

Therefore ∠x = 180-135

m∠x = 45°

∠2 = ∠x (Vertically opposite angles)

∠2 = 45°

Between ∠2 and ∠3 there is an angle, let's call it z.

∠z = ∠1 (Vertically opposite angles)

∠z = 75°

Since the sum of ∠2, ∠z and ∠3 = 180° (Straight angle)

Therefore m∠3 = 180 - (∠2 + ∠z)

m∠3 = 180 - (45 + 75)

m∠3 = 60°

Or in a different way

∠2 + ∠z + ∠3 = 180

45 + 75 + ∠3 = 180

120 + ∠3 = 180

∠3 = 180 - 120

∠3 = 60°

Hope it helps

Answer 2

transverse s at angle 135°

180° - 135° = 45°

Angle 2 is congruent to 45° because they're alternate exterior angles.

transverse t at angle 120°

180° - 120° = 60°

Angle 3 is congruent to 60° because they're alternate exterior angles.

One rule for exterior angles in triangles is that the exterior angle is equal to the sum of the two angles adjacent to the opposite angle of the exterior angle.

135° = angle 1 + 60°

angle 1 = 75°

120° = angle 1 + 45°

angle 1 = 75°

Therefore angle 1 is 75°,angle 2 is 45° and angle 3 is 60°