Question

solve. y = 55 the acute angle measures enter an integer or decimal number more.... find the measure of the acute angle. (3y + 59)° (2y + 11)°

Explanation:

Step1: Set up the equation

Vertical - angles are equal. So, \(3y + 59=2y + 11\).

Step2: Solve for \(y\)

Subtract \(2y\) from both sides of the equation: \(3y-2y+59 = 2y-2y + 11\), which simplifies to \(y+59 = 11\). Then subtract 59 from both sides: \(y=11 - 59=-48\).

Step3: Find the angle - measures

Substitute \(y = - 48\) into the expressions for the angles.
The first angle is \(3y + 59=3\times(-48)+59=-144 + 59=-85\) (not possible as angle - measure cannot be negative in this context, we made a mistake above. The correct relationship for adjacent supplementary angles: \((3y + 59)+(2y + 11)=180\)).

Step4: Correctly set up the equation

\((3y + 59)+(2y + 11)=180\).
Combine like - terms: \(3y+2y+59 + 11=180\), so \(5y+70 = 180\).

Step5: Solve the corrected equation for \(y\)

Subtract 70 from both sides: \(5y=180 - 70=110\).
Divide both sides by 5: \(y=\frac{110}{5}=22\).

Step6: Find the acute angle measure

Substitute \(y = 22\) into \(2y + 11\): \(2\times22+11=44 + 11=55\).
Substitute \(y = 22\) into \(3y + 59\): \(3\times22+59=66+59 = 125\).
The acute angle measure is \(55\) degrees.

Answer:

55