Question

1. blake writes a correct equation to represent the measures of the angles in the diagram.

3t = 90

a. blakes work is shown. what does blake do incorrectly?
3t = 90
3t · 3 = 90 · 3
t = 270

b. show how to solve the equation correctly. use substitution to check your solution.

c. what does the solution represent in this situation?

Explanation:

Part a

To solve the equation \(3t = 90\), we need to isolate \(t\) by performing the inverse operation. The correct operation is to divide both sides by 3, not multiply. Blake multiplied both sides by 3, which is incorrect.

Step 1: Solve the equation \(3t = 90\)

To isolate \(t\), we divide both sides of the equation by 3.
\[
\frac{3t}{3}=\frac{90}{3}
\]

Step 2: Simplify both sides

Simplifying the left side, \(\frac{3t}{3}=t\). Simplifying the right side, \(\frac{90}{3} = 30\). So we get \(t = 30\).

Step 3: Check the solution by substitution

Substitute \(t = 30\) back into the original equation \(3t=90\).
Left side: \(3\times30 = 90\)
Right side: \(90\)
Since the left side equals the right side, the solution is correct.

The diagram shows a right angle (90 degrees) divided into three equal - sized angles, each with measure \(t^{\circ}\). The equation \(3t = 90\) represents the sum of the three angles being equal to the measure of the right angle. So the solution \(t = 30\) represents the measure of each of the three equal - sized angles in the diagram.

Answer:

Blake incorrectly multiplied both sides of the equation \(3t = 90\) by 3 instead of dividing both sides by 3 to isolate \(t\).

Part b