Question

find the measure of each acute angle. (19x - 1)° (13x - 5)° (19x - 1) = □° and (13x - 5) = □°

Explanation:

Step1: Use the property of right - triangle angles

In a right - triangle, the sum of the two acute angles is \(90^{\circ}\). So, \((19x - 1)+(13x - 5)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(19x+13x-1 - 5=90\), which gives \(32x-6 = 90\).

Step3: Solve for \(x\)

Add \(6\) to both sides: \(32x=90 + 6=96\). Then divide both sides by \(32\): \(x=\frac{96}{32}=3\).

Step4: Find the measure of \((19x - 1)\)

Substitute \(x = 3\) into \(19x-1\): \(19\times3-1=57 - 1=56\).

Step5: Find the measure of \((13x - 5)\)

Substitute \(x = 3\) into \(13x-5\): \(13\times3-5=39 - 5=34\).

Answer:

\((19x - 1)=56^{\circ}\) and \((13x - 5)=34^{\circ}\)