Question

The following diagram shows a triangle with each of its sides produced both ways:

What is the sum of degree measures of the angles numbered?

Options

• 720°

• 540°

• 1080°

• 900°

Answer 1

720°

Explanation:

In the given figure

∠1 + ∠x = 180°

Also ∠2 + ∠x = 180°  ......[∠1 = ∠2 vertically opp. angles]

∠1 + ∠x + ∠2 + ∠x = 360°

Similarly, ∠3 + ∠x + ∠4 + z = 360°

And ∠6 + ∠y + ∠y + ∠5 = 360°

Adding all the three equations:

∠1 + ∠2 + 2∠x + ∠3 + ∠4 + 2∠z + ∠5 + ∠6 + 2∠y = 360° + 360° + 360°

∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 + 2(∠x + ∠y + ∠z) = 1080°

∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 + 2(180°) = 1080°

∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 = 1080° – 360° = 720°