Question

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

Explanation:

Step1: Sum of angles in triangle

In a right triangle, the sum of the two acute angles is \(90^\circ\) (since one angle is \(90^\circ\) and the sum of all angles in a triangle is \(180^\circ\)). So, \((19x - 1)+(13x - 5)=90\).

Step2: Solve for x

Combine like terms: \(19x+13x - 1 - 5 = 90\) → \(32x - 6 = 90\).
Add 6 to both sides: \(32x = 90 + 6 = 96\).
Divide by 32: \(x=\frac{96}{32}=3\).

Step3: Find first angle

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

Step4: Find second angle

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

Answer:

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