Question

In the given figure, ∠2 = ∠1 and ∠3 = ∠4. Find ∠θ.

Answer 1

Answer:

The value of ∠θ is [150° - 2(∠1 + ∠3 )].

Step-by-step explanation:

The sum of angles along a straight line is 180°.

It is provided that ∠2 = ∠1 and ∠3 = ∠4.

Compute the value of ∠θ as follows:

∠1 + ∠2 + ∠3 + ∠4 + 30° + θ = 180°

∠1 + ∠1 + ∠3 + ∠3 + 30° + θ = 180°

2∠1 + 2∠3 + 30° + θ = 180°

2∠1 + 2∠3 + θ = 180° - 30°

2(∠1 + ∠3 ) + θ = 150°

θ = 150° - 2(∠1 + ∠3 )

Thus, the value of ∠θ is [150° - 2(∠1 + ∠3 )].