Question

54/55 solve for angle 1 and angle 2. 1 = 92, 2 = 92 1 = 136, 2 = 100 1 = 92, 2 = 46 degrees 1 = 118, 2 = 118 degrees

Explanation:

Step1: Recall angle - sum property of a quadrilateral

The sum of interior angles of a quadrilateral is $360^{\circ}$.

Step2: Find Angle 2

The angle adjacent to the $80^{\circ}$ exterior - angle is $180 - 80=100^{\circ}$ (linear - pair of angles). Since the figure has two pairs of equal - adjacent sides (kites have this property), and the non - vertex angles between the equal sides are equal. Let's assume the quadrilateral is a kite. The angle opposite the $44^{\circ}$ angle is also $44^{\circ}$. Let Angle 2 be $x$. Then, using the angle - sum property of a quadrilateral: $44 + 44+x + 100=360$. Simplifying gives $188 + x=360$, so $x = 360-188 = 172$. But this is wrong. In a kite, the diagonals are perpendicular, and we can also use the fact that the sum of angles around a point is $360^{\circ}$. The correct way is to note that the sum of the interior angles of the quadrilateral is $360^{\circ}$. The angle adjacent to the $80^{\circ}$ exterior angle is $100^{\circ}$. The angle opposite the $44^{\circ}$ angle is $44^{\circ}$. Let's use the property of a kite's symmetry. The two non - vertex angles between the equal sides are equal. Let's call them $\angle1$ and $\angle2$. We know that $44+44 + \angle1+\angle2=360$. Also, since the figure has symmetry, $\angle1=\angle2$. So $88 + 2\angle1=360$. Then $2\angle1=360 - 88=272$, and $\angle1=\angle2 = 136\div2=92^{\circ}$.

Answer:

$1 = 92, 2 = 92$