Question

what is the value of \\(x\\) in the isosceles trapezoid below?

a. 11
b. 26
c. 13
d. 22

Explanation:

Identify trapezoid properties

In an isosceles trapezoid \(ABCD\) with parallel bases \(AB\) and \(CD\), the consecutive interior angles between the parallel bases are supplementary. Therefore, the base angle at vertex \(A\) and the upper base angle at vertex \(C\) (which is equal to the angle at vertex \(D\) by symmetry, or directly using consecutive interior angles along the leg \(BC\) where \(\angle B = \angle A = 2x^\circ\)) satisfy:

$$ \angle B + \angle C = 180^\circ $$

Since \(ABCD\) is an isosceles trapezoid, the base angles are equal:

$$ \angle A = \angle B = 2x^\circ $$

Set up the equation

Using the Supplementary Angles concept, the consecutive interior angles along leg \(BC\) add up to \(180^\circ\):

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

Solve for x

Combine like terms:

$$ 12x + 24 = 180 $$

Subtract 24 from both sides:

$$ 12x = 156 $$

Divide by 12:

$$ x = 13 $$

Answer:

• (A) 11
• (B) 26
• (C) 13 (Correct answer)
• (D) 22