Question

I’m confused I’ve tried doing the equation and get x = 1.75

Answer 1

Solution:

Given:

A parallelogram with;

$\begin{gathered} \angle M=8x+1 \\ \angle K=16x-13 \end{gathered}$

In a parallelogram, the angles on the same side of the transversal are supplementary, which means they add up to 180 degrees.

Hence,

$\angle M+\angle K=180^0$

Thus,

$\begin{gathered} 8x+1+16x-13=180^0 \\ \text{Collecting the like terms,} \\ 8x+16x+1-13=180^0 \\ 24x-12=180 \\ 24x=180+12 \\ 24x=192 \\ \text{Dividing both sides by 24 to get the value of x,} \\ x=\frac{192}{24} \\ x=8 \end{gathered}$

To get the measure of angle K, we substitute the value of x gotten.

$\begin{gathered} \angle K=16x-13 \\ \text{Hence,} \\ m\angle K=16x-13 \\ m\angle K=16(8)-13 \\ m\angle K=128-13 \\ m\angle K=115^0 \end{gathered}$

Therefore, the measure of angle K in the parallelogram is 115 degrees.