Question

solve for the value of n.
(2n+7)°
(3n+3)°
answer attempt 1 out of 2
n =
submit answer

Explanation:

Step1: Identify angle sum

The angles around a point sum to \(360^\circ\), but here we have a right angle (\(90^\circ\)), and the two given angles \((2n + 7)^\circ\) and \((3n + 3)^\circ\), and the straight angle? Wait, no—actually, the three angles (the right angle, \((2n + 7)^\circ\), and \((3n + 3)^\circ\)) should sum to \(180^\circ\)? Wait, no, looking at the diagram, the two angles \((2n + 7)^\circ\) and \((3n + 3)^\circ\) along with the right angle (\(90^\circ\)) form a straight line? Wait, no, the right angle is between two rays, and the other two angles are adjacent. Wait, actually, the sum of \((2n + 7)^\circ\), \(90^\circ\), and \((3n + 3)^\circ\) should be \(180^\circ\)? Wait, no, that can't be. Wait, no—when two lines intersect, but here there's a right angle. Wait, actually, the three angles: \((2n + 7)^\circ\), \(90^\circ\), and \((3n + 3)^\circ\) are adjacent and form a straight angle (180 degrees). So:

\((2n + 7) + 90 + (3n + 3) = 180\)

Step2: Simplify the equation

Combine like terms:

\(2n + 3n + 7 + 3 + 90 = 180\)

\(5n + 100 = 180\)

Step3: Solve for n

Subtract 100 from both sides:

\(5n = 180 - 100\)

\(5n = 80\)

Divide both sides by 5:

\(n = \frac{80}{5}\)

\(n = 16\)

Answer:

\(16\)