Question

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

Answer 1

k or l will be 151 degrees.

j and m are equal to each other, giving you x=1, substitute this in to get j and m equal 29 degrees. k or L are opposite angles meaning they add up to 180 when added to j and m so j+l=180 or m+k=180

Answer 2

Angle K is 151°

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,

`\implies \angle J=\angle M`

⇒ 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°