Question

Quadrilateral GHJK is a rectangle. Find each measure if m<1=37

Answer 1

`\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}`

Step-by-step 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)

`\begin{gathered} m\angle1\text{ + m}\angle2\text{ = 90} \\ m\angle2\text{ = 90-37} \\ m\angle2\text{ = 53} \end{gathered}`

b)

`\begin{gathered} m\angle5\text{ + m}\angle1\text{ = 90} \\ By\text{ transition:} \\ m\angle5\text{ = m}\angle2\text{ = 53} \end{gathered}`

c)

`\begin{gathered} m\angle4\text{ + m}\angle5\text{ = 90} \\ m\angle1\text{ = m}\angle4\text{ = 37} \end{gathered}`
`\begin{gathered} d)\text{ m}\angle3\text{ = m}\angle4\text{ = 37} \\ \text{Base angles of isosceles triangle are equal} \end{gathered}`

d)

`\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}`

e)

`\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}`

f)