Question

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

Explanation:

Step1: Set up equation

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

Step2: Solve for y

Subtract \(2y\) from both sides: \(3y - 2y+59=2y - 2y + 11\), which simplifies to \(y+59 = 11\). Then subtract 59 from both sides: \(y=11 - 59=-48\). But this is incorrect. The correct approach is that the two angles are supplementary (since they form a linear - pair and we want the acute angle). So, \((3y + 59)+(2y+11)=180\).

Step3: Combine like terms

\(3y+2y+59 + 11=180\), which gives \(5y+70 = 180\).

Step4: Isolate y

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

Step5: Find the acute angle

Substitute \(y = 22\) into the expressions for the angles. \(3y+59=3\times22 + 59=66+59 = 125\) and \(2y + 11=2\times22+11=44 + 11=55\). The acute angle is 55 degrees.

Answer:

55