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:

$$
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$$

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:

$$
LATEXBLOCK1
$$

If we find the measure of \(\angle IJK\) when \(x = 11\), we substitute \(x\) into the expression for \(\angle IJK\):

$$m\angle IJK=97+6\times11=97 + 66=163^{\circ}$$