Question

error analysis a student was asked to find m∠1 and m∠2 given that m∠4 = 121°. m∠1=(11x - 35)°, and m∠2=(9x - 4)°. he incorrectly said m∠1 = 19° and m∠2 = 40°. find m∠1 and m∠2. what mistake might the student have made?

Explanation:

Step1: Assume relationship between angles

Assume $\angle1$ and $\angle2$ are supplementary (since no other relationship is given, and we often deal with supplementary - angle situations in geometry problems, i.e., $m\angle1 + m\angle2=180^{\circ}$). So, $(11x - 35)+(9x - 4)=180$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $11x+9x-35 - 4 = 180$, which gives $20x-39 = 180$.

Step3: Solve for x

Add 39 to both sides: $20x=180 + 39=219$. Then $x=\frac{219}{20}=10.95$.

Step4: Calculate $m\angle1$

Substitute $x = 10.95$ into the expression for $m\angle1$: $m\angle1=11x - 35=11\times10.95-35=120.45-35 = 85.45^{\circ}$.

Step5: Analyze the student's error

The student likely made an error in setting up the equation. Maybe they misidentified the relationship between the angles (e.g., thought they were complementary instead of supplementary or vice - versa), or made a calculation error when combining like terms or solving for $x$.

Answer:

$85.45$