Question

1. find the measure of ∠2. 64° 1 3 2 90° 116° 64° 26°

Explanation:

Step1: Identify vertical - angles

$\angle1$ and the $64^{\circ}$ angle are vertical - angles, so $\angle1 = 64^{\circ}$.

Step2: Use triangle - angle sum property

In the triangle with $\angle1$ and $\angle2$, assume the third angle is $\angle3$. Since the two triangles are congruent (by the markings), we know that the sum of angles in a triangle is $180^{\circ}$. In the triangle containing $\angle1$ and $\angle2$, we know that $\angle1+\angle2 + \angle3=180^{\circ}$. Also, note that the two triangles are isosceles (from the markings). But we can also use the fact that the non - congruent angle to $\angle1$ in the other triangle is also $64^{\circ}$. The two triangles together form a quadrilateral. Since $\angle1 = 64^{\circ}$, and considering the relationship between the angles in the figure, $\angle2=116^{\circ}$ because the sum of adjacent angles on a straight line formed by the intersection of the lines in the figure and the angle - sum properties of triangles.

Answer:

$116^{\circ}$