Question

Find the value of x in each case:

Answer 1

`x = 18`

Explanation:

Given:

Angle ABC = 2x

Angle CDE = 8x

Required:

Value of x

SOLUTION:

Line AB is parallel to line CD, therefore, angle ABC and angle BCD are alternate interior angles. Alternate interior angles are equal. Thus:

Angle ABC = Angle BCD = 2x

Since, line BC is parallel to line DE, angle BCD and angle CDE are consecutive interior angles.

Consecutive interior angles are supplementary, therefore:

Angle BCD + Angle CDE = 180°

`2x + 8x = 180`

Use this equation to solve for x

`10x = 180`

Divide both sides by 10

`(10x)/(10) = (180)/(10)`

`x = 18`