Answer:
[tex]\begin{gathered} m\angle2\text{ = 53} \\ m\angle3\text{ = 37} \\ m\angle4\text{ = 37} \\ m\angle5\text{ =53} \\ m\angle6\text{ =106} \\ m\angle7\text{ = 74} \end{gathered}[/tex]Explanation:
Here, we want to find the measure of the given angles
From what we have, the angle marked 1 is of a value 37 degrees
For a rectangle, each angle at the edges equal 90 degrees
That makes a total of 360 degrees
Also, we have four isosceles triangle. These are triangles with equal base angle in each
With these in mind, we can proceed to get the value of the missing indicated angles
a)
[tex]\begin{gathered} m\angle1\text{ + m}\angle2\text{ = 90} \\ m\angle2\text{ = 90-37} \\ m\angle2\text{ = 53} \end{gathered}[/tex]b)
[tex]\begin{gathered} m\angle5\text{ + m}\angle1\text{ = 90} \\ By\text{ transition:} \\ m\angle5\text{ = m}\angle2\text{ = 53} \end{gathered}[/tex]c)
[tex]\begin{gathered} m\angle4\text{ + m}\angle5\text{ = 90} \\ m\angle1\text{ = m}\angle4\text{ = 37} \end{gathered}[/tex][tex]\begin{gathered} d)\text{ m}\angle3\text{ = m}\angle4\text{ = 37} \\ \text{Base angles of isosceles triangle are equal} \end{gathered}[/tex]d)
[tex]\begin{gathered} m\angle6\text{ + m}\angle3\text{ + m}\angle4\text{ = 180} \\ \text{sum of interior angles of a triangle} \\ m\angle6\text{ = 180-37-37} \\ m\angle6\text{ = 106} \end{gathered}[/tex]e)
[tex]\begin{gathered} m\angle6\text{ + m}\angle7\text{ = 180} \\ \text{Sum of angles on a straight line} \\ m\angle7\text{ = 180-106} \\ m\angle7\text{ = 74} \end{gathered}[/tex]f)