Question

1. find the measure of ∠2.

1
2
46°
38°
112°
136°
92°

Explanation:

Step1: Recall sum of angles in quadrilateral

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

Step2: Identify known angles

We know one angle is $90^{\circ}$ (right - angle) and another is $46^{\circ}$. Also, since the markings indicate equal - length sides, we assume it's an isosceles trapezoid - like shape, but we don't need this property for angle calculation. Let the unknown angles be $\angle1$ and $\angle2$.

Step3: Set up equation

Let $\angle1=x$ and $\angle2 = y$. Then $90^{\circ}+46^{\circ}+x + y=360^{\circ}$.

Step4: Solve for $\angle2$

We know that in an isosceles - like situation (from side - length markings), the non - parallel sides' base angles are equal. But we can also just solve the equation. First, simplify the left - hand side: $136^{\circ}+x + y=360^{\circ}$, so $x + y=360^{\circ}-136^{\circ}=224^{\circ}$. Since we don't have any other information about the relationship between $x$ and $y$ other than they are part of the quadrilateral's angles, and if we assume the shape has some symmetry (from the side - length markings), we can consider the non - right and non - $46^{\circ}$ angles are equal. So $\angle2=\frac{224^{\circ}}{2}=112^{\circ}$.

Answer:

$112^{\circ}$