Question

what is the obtuse angle measurement (hint the angle that does not have the numbers inside.) o 142 o 90 (7x - 25)° (4x + 2)°

Explanation:

Step1: Set up equation using vertical - angle property

Vertical angles are equal. So, $4x + 2=7x - 25$.

Step2: Solve for $x$

Subtract $4x$ from both sides: $2 = 3x-25$. Then add 25 to both sides: $27 = 3x$. Divide both sides by 3, we get $x = 9$.

Step3: Find the measure of one of the angles

Substitute $x = 9$ into $4x + 2$. So, $4\times9+2=36 + 2=38^{\circ}$.

Step4: Find the measure of the obtuse angle

The obtuse angle is supplementary to the $38^{\circ}$ angle. Let the obtuse - angle be $y$. Then $y+38^{\circ}=180^{\circ}$. So, $y = 180 - 38=142^{\circ}$.

Answer:

$142$