What is the value of x in the isosceles trapezoid below

Question

asked Jun 8, 2020 180k views

2 Answers

Dimba · Answer 1 · 2020-06-12T20:33:58+0000

Answer:

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
.

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

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.