Question

Find the measure of each acute angle.


(19x − 1)∘ = and (13x − 5)∘ =

Answer 1

34 degrees; 56 degrees

The measures of each of the acute angles are 56 degrees and 34 degrees.

Explanation:

The measures of a triangle add up to 180 degrees.

One angle has the measure of 90 degrees since it is marked as a right angle.

Using this info we can create an equation to solve for x.

(19x-1)+(13x-5)+90=180

Now solve for x.

32x-6+90=180

32x=96

x=3

Now to find the measure of each angle subsitute the value of x.

(19x-1)=19*3-1=56 degrees

(13x-5)=13*3-5=34 degrees

The measures of each of the acute angles are 56 degrees and 34 degrees.

Answer 2

19x - 1 ➡ 19 × 3 - 1 = 56°

13x - 5 ➡ 13 × 3 - 5 = 34°

Explanation:

The given triangle is a right triangle which means one of the angle has a measurement of 90° and since the sum of interior angles in a triangle is equal to 180° the sum of other two angles must be 90°

19x - 1 + 13x - 5 = 90 add like terms

32x - 6 = 90 add 6 to both sides

32x = 96 divide both sides by 32

x = 3

19x - 1 ➡ 19 × 3 - 1 = 56°

13x - 5 ➡ 13 × 3 - 5 = 34°