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 vertical - angle or supplementary - angle relationship (missing info).

Since no relationship between angles is given, assume $\angle1$ and $\angle2$ are supplementary (a common case if not otherwise stated), so $m\angle1 + m\angle2=180^{\circ}$. Then $(11x - 35)+(9x - 4)=180$.

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: Find $m\angle1$.

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

The student likely made an error in setting up the equation for the relationship between $\angle1$ and $\angle2$ or in the algebraic manipulations while solving for $x$.

Answer:

$m\angle1 = 85.45^{\circ}$