Question

What is the answer to this please need answers asap

Answer 1

Case: Geometry: Sum of angles in a triangle

Given: Three angles in a triangle in algebraic format

Required: To find angle K by first solving the resulting algeba

Method: Use sum of angles in a triangle to find x, then plug the value of x to get angle K.

Finding the value of x using sum of angles in a triangle

`\begin{gathered} \measuredangle J\text{ + }\measuredangle K+\text{ }\measuredangle L\text{ = 180}\degree\text{ (Sum of angles in a triangle)} \\ (6x-11)\text{ + (8x-29) + (3x -1) =180}\degree \\ \text{Collecting like terms} \\ 6x+\text{ 8x+3x -11}\degree\text{-29}\degree\text{-1}\degree=\text{ 180}\degree \\ 17x\text{ -41}\degree=180\degree\text{ } \\ 17x=\text{ 180}\degree+41\degree \\ 17x=\text{ 221}\degree \\ \text{Dividing both sides by 17} \\ x=\text{ 13}\degree \end{gathered}`

Finding the angles K

`\begin{gathered} \measuredangle K=\text{ 8x -29}\degree \\ \measuredangle K=\text{ 8(13) -29}\degree \\ \measuredangle K=\text{ 104}\degree\text{ -29}\degree \\ \measuredangle K=75\degree \end{gathered}`

Final answer:

The value of angle K is 75 degrees