Respuesta :
Answer:
[tex]m\angle K \approx 104.14^{\circ}[/tex]
Step-by-step explanation:
In isosceles trapezoid JKLM,
Given: [tex]m\angle J = 17x+7[/tex] and [tex]m\angle M = 11x+13[/tex]
Since, JKLM is an isosceles trapezoid so each pair of base angles is congruent.
[tex]m\angle J = m\angle K[/tex]
[tex]m\angle M = m\angle L[/tex]
As, we know that the sum of the angle of a trapezoid is [tex]360^{\circ}[/tex]
The angles are:
[tex]m\angle J = 17x+7[/tex]
[tex]m\angle K = 17x+7[/tex]
[tex]m\angle L = 11x+13[/tex]
[tex]m\angle M = 11x+13[/tex]
Therefore,
[tex]17x+7+17x+7+11x+13+11x+13 = 360^{\circ}[/tex]
Combine like terms;
[tex]56x + 40 = 360^{\circ}[/tex]
Subtract 40 from both sides we get;
[tex]56x + 40 -40 = 360 - 40[/tex]
Simplify:
[tex]56x = 320[/tex]
Divide both sides by 56 we get;
[tex]x = \frac{320}{56} = \frac{40}{7}[/tex]
To find the angle of [tex]m\angle K[/tex]:
[tex]m\angle K = 17x + 7 = 17(\frac{40}{7}) +7 = 97.14 + 7[/tex]
Simplify:
[tex]m\angle K \approx 104.14^{\circ}[/tex]
Therefore, the value of angle of [tex]m\angle K \approx 104.14^{\circ}[/tex]
Answer:
202
Step-by-step explanation:
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