Question

if m∠ijk=(97 + 6x)°, find the requested values.

Explanation:

Step1: Set up the equation

Assume \(97 + 6x=(-x + 73)+(156-5x)\)

Step2: Combine like - terms on the right - hand side

\[97 + 6x=-6x+229\]

Step3: Move \(x\) terms to one side

\[6x+6x=229 - 97\]

Step4: Simplify both sides

\[12x=132\]

Step5: Solve for \(x\)

\[x = 11\]

Step6: Find the measure of \(\angle IJK\)

\[m\angle IJK=97+6\times11 = 163^{\circ}\]

Answer:

Assuming the three - angle measures around point J sum to 360° (since they form a full - turn), we first set up the equation:
\[

$$\begin{align*} (97 + 6x)+(-x + 73)+(156-5x)&=360\\ 97+6x - x+73 + 156-5x&=360\\ (6x - x-5x)+(97 + 73+156)&=360\\ 0x+(170 + 156)&=360\\ 326&=360 \end{align*}$$

\]
This is incorrect. Let's assume the angles are part of a linear - pair or some other relationship. If they are a linear - pair (sum to 180°), we need more information about which two angles are related. But if we assume that \(\angle IJK\) is the sum of the other two angles:
\[

$$\begin{align*} 97 + 6x&=(-x + 73)+(156-5x)\\ 97 + 6x&=-x - 5x+73 + 156\\ 97 + 6x&=-6x+229\\ 6x+6x&=229 - 97\\ 12x&=132\\ x& = 11 \end{align*}$$

\]
If we find the measure of \(\angle IJK\) when \(x = 11\), we substitute \(x\) into the expression for \(\angle IJK\):
\[m\angle IJK=97+6\times11=97 + 66=163^{\circ}\]