Question

Find the measure of each interior angle using the given information

Answer 1

Step 1:

The sum of angles in any quadrilateral is 360 degrees

Step 2:

Add all the angles and equate it to 360

`\begin{gathered} 2x\text{ + 15 + x + 15 + 3x - 20 + x = 360} \\ 7x\text{ +10 = 360} \\ 7x\text{ = 360 -10} \\ 7x\text{ = }350 \\ x\text{ = }(350)/(7) \\ x\text{ = }50 \end{gathered}`

Final answer

Next, find each angle

`\begin{gathered} ^{\angle J\text{ = 2x + 15 = 2}*50\text{ +15}}\text{ = 100 + 15 = 115} \\ \angle\text{x = 50, }\angle K\text{ = 3}*50\text{ - 20 = 150 - 20 =13}0 \\ \angle N\text{ = x + 15 = 50 + 15 = 65} \end{gathered}`
`\begin{gathered} \angle J\text{ = 115} \\ \angle M\text{ = 50} \\ \angle K\text{ = 130} \\ \angle N\text{ = 65} \end{gathered}`