KEVI is an isosceles trapezoid. If KN 10, NV = x, and IE = 2x+6,

what is the length of KV?

14

Step-by-step explanation:

A trapezoid is a quadrilateral (has four sides and four angles) with a pair of opposite parallel sides. The pair of opposite parallel side is known as the base.

An isosceles trapezoid is a trapezoid with equal legs. The diagonals are also equal and both the upper and lower base angles are congruent.

From the question:

KV = IE = 2x + 6 (diagonals of a trapezoid are congruent)

From line segment addition postulate:

KV = KN + NV

substituting:

2x + 6 = 10 + x

2x + 6 - x = 10

x + 6 = 10

x = 10 - 6

x = 4

KV = 2x + 6

substituting x = 4:

KV = 2(4) + 6

KV = 14

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step-by-step explanation: