Question

find the measure of the obtuse angle.
solve. ( y = )
the obtuse angle measures degrees.

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. But here, \((3y + 6)\) and \((2y+89)\) are supplementary (they form a linear - pair). So, \((3y + 6)+(2y + 89)=180\).

$$\begin{align*} 3y+6 + 2y+89&=180\\ 5y+95&=180 \end{align*}$$

Step2: Solve for \(y\)

Subtract 95 from both sides: \(5y=180 - 95\), so \(5y = 85\). Then divide both sides by 5: \(y=\frac{85}{5}=17\).

Step3: Find the obtuse angle

Substitute \(y = 17\) into \(3y + 6\): \(3\times17+6=51 + 6=57\) (acute). Substitute \(y = 17\) into \(2y+89\): \(2\times17+89=34 + 89 = 123\).

Answer:

\(y = 17\); The obtuse angle measures \(123\) degrees.