Question

1. find the missing angle. m j 79° l k? degrees

Explanation:

Step1: Recall quadrilateral angle - sum property

The sum of the interior angles of a quadrilateral is 360°. Assume the missing angle $\angle K = x$, and if we assume $\angle M$ and $\angle L$ are supplementary (a common case in trapezoids, if it is a trapezoid; without more information, we assume the other two non - given angles are equal), and since $\angle J=79^{\circ}$. Let's assume the other two non - given angles are equal for simplicity. Let the sum of the two non - given angles be $y$. Then $y + 79^{\circ}=360^{\circ}$.

Step2: Calculate the sum of the two non - given angles

$y=360^{\circ}-79^{\circ}=281^{\circ}$. If the two non - given angles $\angle M$ and $\angle L$ are equal, then $x=\frac{281^{\circ}}{2}=101^{\circ}$ (assuming the figure is an isosceles trapezoid). In a general quadrilateral, if we assume the other two angles are equal, we first find the sum of the non - known angles. The sum of the interior angles of a quadrilateral $S = 360^{\circ}$. Let the missing angle be $\theta$. We know one angle is $79^{\circ}$. Let the sum of the remaining three angles be $A$. Then $A=360^{\circ}-79^{\circ}=281^{\circ}$. If the other two non - shown angles are equal, then $\theta = 101^{\circ}$ (because we assume the non - $79^{\circ}$ part is split evenly between two equal angles in a symmetric case like an isosceles trapezoid). In a more general sense, without further information about the figure, if we assume the non - $79^{\circ}$ part is split into two equal parts (a reasonable assumption when no other details are given), we have:
Let the sum of the three non - known angles be $S_{1}=360 - 79=281^{\circ}$. If the two non - shown non - $79^{\circ}$ angles are equal, each of those angles (including the missing angle) is $\frac{360 - 79}{2}=101^{\circ}$

Answer:

$101$