Answer:
Since it is an isosceles trapezoid, the Angle K = Angle J = 118
Since it is a trapezoid, all 4 angles total 360.
Anlge K + Angle J = 236
Angle L + M = 360 - 236 = 124
Angle L = 62 and Angle M = 62
Step-by-step explanation:
You can use the symmetric property of the isosceles trapezoid and the fact that a triangle has sum of its angles as 180°
The measures of unknown angles are:
[tex]m\angle L = 62^\circ\\ m\angle M = m\angle L = 62^\circ\\ m\angle J = m \angle K = 118^\circ[/tex]
Due to the figure being isosceles trapezoid, it is symmetric.
Isosceles trapezoid has its two rest sides(which aren't necessary parallel) are of equal length.
Considering JKLM trapezoid, we have:
[tex]m\angle J = m \angle K\\ m\angle M = m\angle L[/tex]
Thus, we have:
[tex]m\angle J = m\angle K = 118^\circ[/tex]
(Refer to the diagram attached below)
Dropping perpendiculars from vertices J and K on line LM at A and B respectively, we get:
[tex]m\angle JKA = m\angle KAL = 90^\circ \text{\: (Since the angles are alternate interior angles)}\\ m\angle LKA = m\angle JKL - m\angle JKA = 118 - 90 = 28^\circ\\ [/tex]
Since in any triangle, we have sum of all the angles as of 180 degrees, thus:
[tex]m\angle KLA + m\angle KAL + m\angle AKL = 180^\circ\\ m\angle KLA +90^\circ + 28^\circ = 180^\circ\\ m\angle KLA = 62^\circ [/tex]
Since angle L and angle M are of same measure, thus:
[tex]m\angle KLA = m\angle JMB = 62^\circ[/tex]
Thus, we have the missing angles as:
[tex]m\angle L = 62^\circ\\ m\angle M = m\angle L = 62^\circ\\ m\angle J = m \angle K = 118^\circ[/tex]
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