Question

find the values of x and the missing angle measurement. (pictures may not be to scale)

Explanation:

Step1: Use the property of complementary angles

Since the two angles \(A = 72^{\circ}\) and \(B=(3x + 3)^{\circ}\) are complementary (they form a right - angle, so \(A + B=90^{\circ}\)).
We substitute the values into the equation: \(72+(3x + 3)=90\).

Step2: Simplify the equation

First, combine like terms: \(3x+75 = 90\).
Then, subtract 75 from both sides: \(3x=90 - 75\), so \(3x = 15\).

Step3: Solve for \(x\)

Divide both sides by 3: \(x=\frac{15}{3}=5\).

Step4: Find the measure of \(\angle B\)

Substitute \(x = 5\) into the expression for \(\angle B\): \(\angle B=(3x + 3)^{\circ}\).
\(\angle B=(3\times5+3)^{\circ}=(15 + 3)^{\circ}=18^{\circ}\).

Answer:

\(x = 5\) and \(\angle B=18^{\circ}\)