Question

find the value of x.
5)
(3 + 4x)°
31°
a) 13
b) 11
c) 14
d) 16

Explanation:

Step1: Identify angle relationship

The angles \(31^\circ\), \((3 + 4x)^\circ\), and the right angle (\(90^\circ\)) are related such that their sum is \(180^\circ\) (linear pair or supplementary angles around a point). Wait, actually, looking at the diagram, the two angles \(31^\circ\) and \((3 + 4x)^\circ\) along with the right angle should add up to \(180^\circ\)? Wait, no, maybe the sum of \(31^\circ\), \((3 + 4x)^\circ\) and \(90^\circ\) is \(180^\circ\)? Wait, no, let's correct. The three angles: \(31^\circ\), \((3 + 4x)^\circ\), and the right angle (since there's a right angle symbol) should add up to \(180^\circ\) (because they are on a straight line, supplementary). So:
\(31 + (3 + 4x) + 90 = 180\)? Wait, no, maybe the two angles \(31^\circ\) and \((3 + 4x)^\circ\) add up to \(90^\circ\) because they are complementary to the right angle? Wait, the right angle is \(90^\circ\), so the sum of \(31^\circ\) and \((3 + 4x)^\circ\) should be \(90^\circ\) (since they form a right angle together). Let's check that.

So, \(31 + (3 + 4x) = 90\)

Step2: Solve the equation

Simplify the left side: \(31 + 3 + 4x = 90\)

\(34 + 4x = 90\)

Subtract 34 from both sides: \(4x = 90 - 34\)

\(4x = 56\)

Divide both sides by 4: \(x = \frac{56}{4} = 14\)

Answer:

C) 14