Question

error analysis in exercises 15 and 16, describe and correct the error in using the diagram to find the value of x.

15.
$(13x + 45)^\circ + (19x + 3)^\circ = 180^\circ$
$32x + 48 = 180$
$32x = 132$
$x = 4.125$

Explanation:

Step1: Identify correct angle relationship

The angles \((13x + 45)^\circ\) and \((19x + 3)^\circ\) are vertical angles, so they are congruent (equal in measure), not supplementary.

Step2: Set up correct equation

$$13x + 45 = 19x + 3$$

Step3: Isolate variable terms

Subtract \(13x\) from both sides:
$$45 = 6x + 3$$

Step4: Isolate constant terms

Subtract 3 from both sides:
$$42 = 6x$$

Step5: Solve for x

Divide both sides by 6:
$$x = \frac{42}{6} = 7$$

Answer:

The error was incorrectly classifying vertical angles as supplementary (summing to \(180^\circ\)). Vertical angles are equal, so the correct equation gives \(x = 7\).