Question

1. solve for x. (4x + 7)° (2x + 5)° diagram of intersecting lines/angles

Explanation:

Step1: Identify angle relationship

The two angles \((4x + 7)^\circ\) and \((2x + 5)^\circ\) are complementary to the right angle? Wait, no, looking at the diagram, the vertical line and the horizontal? Wait, actually, the two angles \((4x + 7)^\circ\) and \((2x + 5)^\circ\) along with the right angle? Wait, no, the diagram shows a vertical line (16 is probably a typo or label) and two angles on either side, forming a right angle? Wait, no, actually, the two angles \((4x + 7)^\circ\) and \((2x + 5)^\circ\) should add up to \(90^\circ\) because they are adjacent and form a right angle (since the line is vertical, maybe the other line is horizontal, so the angles between them are complementary). So:
\(4x + 7 + 2x + 5 = 90\)

Step2: Combine like terms

Combine the \(x\) terms and the constant terms:
\(6x + 12 = 90\)

Step3: Subtract 12 from both sides

\(6x = 90 - 12\)
\(6x = 78\)

Step4: Divide by 6

\(x = \frac{78}{6}\)
\(x = 13\)

Answer:

\(x = 13\)