Angle j and angle m are base angles of an isosceles trapezoid jklm. if angle j=20x+9 and angle m =14x+15, find angle k

Angle K is 151°

Step-by-step explanation:

Given :

JKLM is an isosceles trapezoid,

In which base angles ( either top or bottom ) are,

∠J=20x+9 and  ∠M =14x+15,

In an isosceles triangle the angles on either side of the bases are the same measure,

⇒ 20x + 9 = 14x + 15

⇒ 20x - 14x = 15 - 9

⇒ 6x = 6

⇒ x = 1

Thus, the angles are,

⇒ ∠J = ∠M = 20 + 9 = 29°,

Let ∠K = ∠L = x,

By the property of quadrilateral,

∠J + ∠M + ∠K + ∠L = 360°

⇒ 29° + 29° + x + x = 360°

⇒ 58° + 2x = 360°

⇒ 2x = 302°

⇒ x = 151°

Hence, ∠K = 151°

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step-by-step explanation: