Question

In the given figure l parallel m and t is transversal. If angle 1 and angle 2 are in the ratio 5:7, find the measure of the angles 1,2,3,8.​

Answer 1

1:2=5:7,

1=5×180÷12=75

2=7×180÷12=105

3=1=75

8=2=105

Answer 2

Answer:

∠1 =∠3=60° and  ∠ 2=∠8 = 120°.

Step-by-step explanation:

We are given that ∠1 and ∠ 2 are in the ratio 1 : 2

Let the ratio be x

So, the angles are x and 2x

Since ∠1 and ∠ 2 are linear pair

So, ∠1 +∠ 2 = 180°

So, x+2x=180°

3x=180°

x=60°

So, ∠1 =60°

∠ 2 = 2x = 2*60 = 120°

∠1 =∠3 (vertically opposite angles)

∠1 =∠3=60°

Since l || m

So, ∠ 2=∠ 6(Corresponding angles)

∠ 2=∠6= 120°

Now , ∠6 = ∠8  (vertically opposite angles)

So,  ∠6 = ∠8 = 120°

Hence ∠1 =∠3=60° and  ∠ 2=∠8 = 120°.