Question

problem solving with addition and subtraction equations

1. adesh writes the correct equation to represent the angle measures in the diagram.

\\( m + 33 = 90 \\)

a. solve the equation. use substitution to check your solution.

b. what does the solution represent in this situation?

c. adesh’s work is shown. what does adesh do incorrectly?
\\( m + 33 = 90 \\)
\\( m + 33 + 33 = 90 + 33 \\)
\\( m = 123 \\)

Explanation:

Step1: Isolate $m$ via subtraction

Subtract 33 from both sides:
$m + 33 - 33 = 90 - 33$

Step2: Calculate the value of $m$

$m = 57$

Step3: Verify via substitution

Substitute $m=57$ into original equation:
$57 + 33 = 90$
$90 = 90$ (true)

Step4: Interpret the solution

The solution represents the unknown angle measure $m^\circ$ that, when added to $33^\circ$, forms a right angle (90°).

Step5: Identify Adesh's error

Instead of subtracting 33 from both sides to isolate $m$, Adesh incorrectly added 33 to both sides, which violates the equality property of equations.

Answer:

a. $m = 57$ (verified as correct by substitution)
b. The solution represents the measure of the unknown angle $m^\circ$ in the right angle diagram.
c. Adesh incorrectly added 33 to both sides of the equation instead of subtracting 33 to isolate $m$.