Question

Find the value of x in each case:

Answer 1

Answer:

$x = 18$

Step-by-step 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

$\frac{10x}{10} = \frac{180}{10}$

$x = 18$