Question

Which postulate or theorem justifies this statement: ∠ 11 + ∠ 10 = 180°

A. Linear Pair postulate

B. Alternate Interior Angles theorem

C. Vertical Angles theorem

D. Same-side Interior Angles theorem

Answer 1

Same-side Interior Angles theorem justifies ∠ 11 + ∠ 10 =180°

Explanation:

To Prove:

∠ 11 + ∠ 10 =180°

Proof:

Consider lines are Parallel,then

Corresponding Angles are Equal

∴ ∠ 10 = ∠ 12 say (equation 1)

Now by Linear Pair postulate we have,

∴ ∠ 11 + ∠ 12 = 180° say (equation 2)

Now by replacing ∠12 by ∠ 10 from equation 1 in equation 2 we get

∴ ∠ 11 + ∠ 10 = 180°

Hence proved the above statement.