Question

in the given figure l || q.and t is a transversal such that the values of ∆1 and ∆2 are in the ratio 2 : 4 Find the measure of all the angles marked from 1 to 8​

Answer 1

Answer:

Step-by-step explanation:

2:4 will be 2x + 4x

2x+4x=180°

6x=180°

x=180°/6= 30°

x=30°

Δ1 and Δ2 are Corresponding angle

Δ4 and Δ1 is Corresponding angle

Δ3 and Δ2 are Corresponding

so, they can change the angles and intersect with each other within the radius of 2:4 ratio

Hope It helps you!!

Answer 2

Angle 1 = Angle 3 = angle 5 = angle 7 = 60°

and

Angle 2 = angle 4 = angle 6 = angle 8 = 120°

Step-by-step explanation:

As angle 1 and angle 2 are in the ratio 2:4 => 1:2 and they form a linear pair, therefore

x + 2x = 180°

3x = 180°

x = 60°

Therefore Angle 1 = 60°

And angle 2 = 60° x 2 = 120°

Now angle 1 and angle 3 form vertically opposite angles, therefore Angle 1 = angle 3 = 60°

Similarly angle 2 = angle 4 = 120°

Now angle 4 = angle 6 (Alternate interior angles)

Therefore Angle 6 = 120°

Similarly angle 3 = angle 5 = 60°

Now angle 6 = angle 8 (Vertically opposite angles)

Therefore angle 8 = 120°

Similarly angle 5 = angle 7

Therefore angle 7 = 60°

Hope you find it easy