Question

if $m\angle3$ is $-5(x + 3)$ degrees and $m\angle6$ is $x - 33$ degrees, what is $x$?

Explanation:

Step1: Identify the relationship between angles

Angles \( \angle3 \) and \( \angle6 \) are supplementary (they form a linear - pair). So \( m\angle3 + m\angle6=180^{\circ}\).

Step2: Substitute the given expressions

Given \( m\angle3=-5(x + 3)\) and \( m\angle6=x - 33\). Then \(-5(x + 3)+(x - 33)=180\).

Step3: Expand the equation

Expand \(-5(x + 3)\) using the distributive property \(a(b + c)=ab+ac\). We get \(-5x-15+x - 33 = 180\).

Step4: Combine like terms

Combine the \(x\) - terms \((-5x+x=-4x)\) and the constant terms \((-15-33=-48)\). The equation becomes \(-4x-48 = 180\).

Step5: Isolate the variable term

Add \(48\) to both sides of the equation: \(-4x-48 + 48=180 + 48\), which simplifies to \(-4x=228\).

Step6: Solve for \(x\)

Divide both sides by \(-4\): \(x=\frac{228}{-4}=- 57\).

Answer:

\(x=-57\)