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viktelen [127]
3 years ago
5

What is the value of x in the isosceles trapezoid below

Mathematics
1 answer:
Nookie1986 [14]3 years ago
8 0

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 <em>CD is parallel to AB</em>.

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.

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