Question

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

Answer 1

Answer:

$m\angle K \approx 104.14^{\circ}$

Step-by-step 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;

$x = \frac{320}{56} = \frac{40}{7}$

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

$m\angle K = 17x + 7 = 17(\frac{40}{7}) +7 = 97.14 + 7$

Simplify:

$m\angle K \approx 104.14^{\circ}$

Therefore, the value of angle of $m\angle K \approx 104.14^{\circ}$

Answer 2

Answer:

202

Step-by-step explanation:

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