Question

find the value of x.
53°
(3x + 4)°
x =

Explanation:

Step1: Identify angle - sum relationship

The two angles \(53^{\circ}\) and \((3x + 4)^{\circ}\) are complementary (since the angle at \(G\) is a right - angle, \(90^{\circ}\)). So, \(53+(3x + 4)=90\).

Step2: Simplify the left - hand side

Combine like terms: \(53+3x + 4=3x+57\). So, the equation becomes \(3x + 57=90\).

Step3: Isolate the variable term

Subtract 57 from both sides of the equation: \(3x=90 - 57\).
\(3x=33\).

Step4: Solve for \(x\)

Divide both sides by 3: \(x=\frac{33}{3}\).

Answer:

\(x = 11\)