Question

error analysis a student was asked to find m∠a and m∠b given that m∠d = 121°. m∠a=(11x - 29)°, and m∠b=(9x - 10)°. she incorrectly said m∠a = 25° and m∠b = 34°. find m∠a and m∠b. what mistake might the student have made? m∠a = □°

Explanation:

Step1: Assume relationship between angles

Since no information about the relationship between $\angle A$, $\angle B$ and $\angle D$ is given in the problem - statement, we assume that $\angle A+\angle B$ and $\angle D$ are related by some geometric property. If we assume that $\angle D$ is an exterior - angle of a triangle with $\angle A$ and $\angle B$ as non - adjacent interior angles, then $\angle D=\angle A+\angle B$ (by the exterior - angle property of a triangle). So, $(11x - 29)+(9x - 10)=121$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $(11x+9x)+(-29 - 10)=121$, which gives $20x-39 = 121$.

Step3: Solve for x

Add 39 to both sides of the equation: $20x-39 + 39=121 + 39$, so $20x=160$. Then divide both sides by 20: $x=\frac{160}{20}=8$.

Step4: Find m∠A

Substitute $x = 8$ into the expression for $\angle A$: $m\angle A=11x - 29=11\times8-29=88 - 29 = 59^{\circ}$.

Answer:

$59$