Question

What is the value of x in the isosceles trapezoid below

Answer 1

13

Explanation:

a pex

Answer 2

D. 13

Explanation:

From the diagram,
`\angle BAD=2x\degree` and
`\angle BCD=(10x+24)\degree`

In an isosceles trapezium, the base angles are equal.

This implies that
`\angle ABC=\angle BAD`
`\implies \angle ABC=2x\degree`

The side length CB of the trapezoid is a transversal line because CD is parallel to AB.

This means that
`\angle ABC=2x\degree` and
`\angle BCD=(10x+24)\degree` are co-interior angles.

Since co-interior angles are supplementary, we write and solve the following equation for
`x`.

`2x\degree+(10x+24)\degree=180\degree`

Group similar terms

`2x+10x=180-24`

Simplify both sides of the equation.

`12x=156`

Divide both sides by 12

`(12x)/(12)=(156)/(12)`

`\therefore x=13`

The correct answer is D.