Question

solve for the value of q.
(q+2)°
(3q-2)°
answer attempt 1 out of 2
q =
submit answer

Explanation:

Step1: Identify angle relationship

The two angles form a right angle (90°), so their sum is 90°. Thus, \((q + 2) + (3q - 2) = 90\).

Step2: Simplify the equation

Combine like terms: \(q + 3q + 2 - 2 = 90\) → \(4q = 90\)? Wait, no, wait: \(q + 2 + 3q - 2 = 4q\), so \(4q = 90\)? Wait, no, wait, the angles are \((q + 2)^\circ\) and \((3q - 2)^\circ\), and they add up to 90° (since the vertical line suggests a right angle). So:
\((q + 2) + (3q - 2) = 90\)
Simplify: \(q + 3q + 2 - 2 = 90\) → \(4q = 90\)? Wait, that can't be. Wait, maybe I made a mistake. Wait, \(q + 2 + 3q - 2 = 4q\), so \(4q = 90\)? No, wait, 90 divided by 4 is 22.5? Wait, no, maybe the angles are complementary? Wait, the diagram shows two angles with a vertical line, so they form a right angle, so their sum is 90 degrees. So:

\((q + 2) + (3q - 2) = 90\)

Simplify: \(q + 3q + 2 - 2 = 90\) → \(4q = 90\)? Wait, that would be \(q = 22.5\), but that seems odd. Wait, maybe I misread the angles. Wait, the angles are \((q + 2)^\circ\) and \((3q - 2)^\circ\), and they are adjacent to form a right angle (90°). So:

\((q + 2) + (3q - 2) = 90\)

Simplify: \(q + 3q + 2 - 2 = 4q\), so \(4q = 90\) → \(q = 90 / 4 = 22.5\)? Wait, but maybe the angles are supplementary? No, the vertical line suggests a right angle. Wait, maybe the diagram is a straight line? No, the vertical line has an arrow up and down, so it's a straight line? Wait, no, the vertical line with an arrow up and an arrow down is a straight line (180°), but the other angle is between them. Wait, maybe the two angles are supplementary? Wait, if the vertical line is a straight line (180°), then the two angles add up to 180°? Wait, that would make more sense. Wait, the diagram: one arrow up, one arrow down, so it's a straight line (180°), and the two angles are \((q + 2)^\circ\) and \((3q - 2)^\circ\), so they add up to 180°? Wait, that would be:

\((q + 2) + (3q - 2) = 180\)

Simplify: \(q + 3q + 2 - 2 = 4q\) → \(4q = 180\) → \(q = 45\). Ah, that makes sense! I misread the diagram. The vertical line with arrows up and down is a straight line (180°), so the two angles are supplementary (add to 180°). So:

Step1: Correct angle relationship

The two angles form a straight line (180°), so their sum is 180°. Thus: \((q + 2) + (3q - 2) = 180\)

Step2: Simplify the equation

Combine like terms: \(q + 3q + 2 - 2 = 4q\), so \(4q = 180\)

Step3: Solve for q

Divide both sides by 4: \(q = \frac{180}{4} = 45\)

Yes, that makes sense. So the angles are \((45 + 2) = 47^\circ\) and \((3*45 - 2) = 133^\circ\), and 47 + 133 = 180, which is correct for a straight line.

Answer:

\(q = 45\)