Answer:
D. 13
Step-by-step explanation:
From the diagram, [tex]\angle BAD=2x\degree[/tex] and [tex]\angle BCD=(10x+24)\degree[/tex]
In an isosceles trapezium, the base angles are equal.
This implies that [tex]\angle ABC=\angle BAD[/tex] [tex]\implies \angle ABC=2x\degree[/tex]
The side length CB of the trapezoid is a transversal line because CD is parallel to AB.
This means that [tex]\angle ABC=2x\degree[/tex] and [tex]\angle BCD=(10x+24)\degree[/tex] are co-interior angles.
Since co-interior angles are supplementary, we write and solve the following equation for [tex]x[/tex].
[tex]2x\degree+(10x+24)\degree=180\degree[/tex]
Group similar terms
[tex]2x+10x=180-24[/tex]
Simplify both sides of the equation.
[tex]12x=156[/tex]
Divide both sides by 12
[tex]\frac{12x}{12}=\frac{156}{12}[/tex]
[tex]\therefore x=13[/tex]
The correct answer is D.
