Question

find the measure of each acute angle.
(11x - 2) = □□ and (6x + 7) = □□

Explanation:

Step1: Use the property of right - angled triangle

In a right - angled triangle, the sum of the two acute angles is \(90^{\circ}\). So, \((11x - 2)+(6x + 7)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(11x+6x-2 + 7=90\), which gives \(17x+5 = 90\).

Step3: Solve for \(x\)

Subtract \(5\) from both sides: \(17x=90 - 5=85\). Then divide both sides by \(17\): \(x=\frac{85}{17}=5\).

Step4: Find the measure of \((11x - 2)^{\circ}\)

Substitute \(x = 5\) into \(11x-2\): \(11\times5-2=55 - 2=53\).

Step5: Find the measure of \((6x + 7)^{\circ}\)

Substitute \(x = 5\) into \(6x + 7\): \(6\times5+7=30 + 7=37\).

Answer:

\((11x - 2)=53^{\circ}\) and \((6x + 7)=37^{\circ}\)