Question

find the measure of the obtuse angle. solve. y = the obtuse angle measures degrees. (3y - 5)° (5y + 25)°

Explanation:

Step1: Set up the equation

Vertical - angles are equal. So, \(3y - 5=5y + 25\).

Step2: Solve for \(y\)

Subtract \(3y\) from both sides: \(-5 = 2y+25\). Then subtract 25 from both sides: \(-5 - 25=2y\), so \(-30 = 2y\). Divide both sides by 2: \(y=-15\).

Step3: Find the measure of an angle

Substitute \(y = - 15\) into \(3y - 5\): \(3(-15)-5=-45 - 5=-50\) (This is wrong. We should use the fact that the angles are supplementary since we want the obtuse - angle situation. Let's assume the two angles are supplementary, so \((3y - 5)+(5y + 25)=180\)).

Step4: Solve the new equation for \(y\)

Combine like - terms: \(8y+20 = 180\). Subtract 20 from both sides: \(8y=160\). Divide both sides by 8: \(y = 20\).

Step5: Find the measure of the obtuse angle

Substitute \(y = 20\) into \(5y + 25\): \(5(20)+25=100 + 25=125\).

Answer:

125