Question

In isosceles trapezoid JKLM, m∠J = 17x + 7, and m∠M = 11x + 13. Find m∠K.

Answer 1

202

Explanation:

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Answer 2

`m\angle K \approx 104.14^(\circ)`

Explanation:

In isosceles trapezoid JKLM,

Given:
`m\angle J = 17x+7` and
`m\angle M = 11x+13`

Since, JKLM is an isosceles trapezoid so each pair of base angles is congruent.

`m\angle J = m\angle K`

`m\angle M = m\angle L`

As, we know that the sum of the angle of a trapezoid is
`360^(\circ)`

The angles are:

`m\angle J = 17x+7`

`m\angle K = 17x+7`

`m\angle L = 11x+13`

`m\angle M = 11x+13`

Therefore,

`17x+7+17x+7+11x+13+11x+13 = 360^(\circ)`

Combine like terms;

`56x + 40 = 360^(\circ)`

Subtract 40 from both sides we get;

`56x + 40 -40 = 360 - 40`

Simplify:

`56x = 320`

Divide both sides by 56 we get;

`x = (320)/(56) = (40)/(7)`

To find the angle of
`m\angle K`:

`m\angle K = 17x + 7 = 17((40)/(7)) +7 = 97.14 + 7`

Simplify:

`m\angle K \approx 104.14^(\circ)`

Therefore, the value of angle of
`m\angle K \approx 104.14^(\circ)`