Question

Given angles ∠1 = 10x + 1 and ∠2 = x + 3 as a linear pair. Prove that x = 16.

Answer 1

By using the property that the sum of angles in a linear pair equals 180 degrees, we set up an equation with the given angle expressions, combine like terms, and solve for x to prove that x is indeed 16.

Step-by-step explanation:

To prove that x = 16, given that angles ∠1 and ∠2 form a linear pair and have the expressions ∠1 = 10x + 1 and ∠2 = x + 3, we need to use the property that the sum of angles in a linear pair equals 180 degrees.

First, set up the equation based on the linear pair property:

• 10x + 1 + x + 3 = 180

Combine like terms:

• 11x + 4 = 180

Subtract 4 from both sides:

• 11x = 176

Divide both sides by 11:

• x = 16

Through this process, we have proven that x must be 16 for the given conditions to hold true.

To prove that x = 16, we need to show that angles ∠1 and ∠2 form a linear pair. A linear pair consists of two adjacent angles that add up to 180 degrees.

So, ∠1 + ∠2 = (10x + 1) + (x + 3) = 11x + 4. If ∠1 and ∠2 are a linear pair, then their sum should be equal to 180 degrees.

11x + 4 = 180. Solve this equation for x to find that x = 16.