Consider the following diagram. Point Q is equidistant from A and B. If the distance from A to the perpendicular line is 3/4x+6 and the distance from B to the same perpendicular line is 5x-4/5. What is the value of x?

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

Step-by-step 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.