Question

Find the measure of each acute angle. (3x + 2)∘ = and x∘ =

Answer 1

Answer:

        22°  and  68°

Step-by-step explanation:

x° + (3x+2)° + 90° = 180°

(4x)° + 2° = 90°

(4x)° = 88°

x° = 22°

(3x+2)° = (3×22+2) = 68°

Answer 2

Answer:

The measure of one of the acute angles is 22 degrees, and the measure of the other acute angle is 68 degrees.

Step-by-step explanation:

The angles of a triangle add up to 180 degrees; we know this by the Sum of Angles of a Triangle Theorem.

Then one angle is marked as a right angle meaning it has a measure of 90 degrees.

Using this information and the labels on the diagram we can set up an equation:

x+3x+2+90=180

Now we can solve for x.

4x+92=180

4x=88

x=22 degrees

The measure of one of the acute angles is 22 degrees.

Now to solve for the measure of the other acute angle.

Subsitute the value of x first.

x=22

(3x+2)=?

3*22+2=68 degrees

The measure of the other acute angle is 68 degrees.