what is m∠i? m∠i = °
what is m∠i? m∠i = °
Answer
Answer:
$77$
Explanation:
Step1: Use the property of inscribed - angles
In a circle, inscribed angles that intercept the same arc are equal. $\angle H$ and $\angle I$ intercept the same arc $\overset{\frown}{GJ}$, so $2x - 55=x + 6$.
Step2: Solve the equation for $x$
Subtract $x$ from both sides: $2x-x-55=x - x+6$, which simplifies to $x-55 = 6$. Then add 55 to both sides: $x=6 + 55=61$.
Step3: Find the measure of $\angle I$
Substitute $x = 61$ into the expression for $\angle I$. $\angle I=x + 6$. So $\angle I=61+6=77^{\circ}$.