Question

What is the value of x in the isosceles trapezoid below

Answer 1

Answer:

D. 13

Step-by-step 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

$\frac{12x}{12}=\frac{156}{12}$

$\therefore x=13$

The correct answer is D.