Question

in circle $z$, $m\angle xyw = 43^\circ$. solve for $x$ if $m\overset{\frown}{xw} = (7x + 46)^\circ$. if necessary, round your answer to the nearest tenth.
answer
attempt 1 out of 2
$x = $

Explanation:

Step1: Apply inscribed angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc, so $m\angle XYW = \frac{1}{2}m\overset{\frown}{XW}$.

Step2: Substitute given values

Substitute $m\angle XYW=43^\circ$ and $m\overset{\frown}{XW}=(7x+46)^\circ$:
$43 = \frac{1}{2}(7x + 46)$

Step3: Multiply both sides by 2

Eliminate the fraction:
$43 \times 2 = 7x + 46$
$86 = 7x + 46$

Step4: Isolate the term with x

Subtract 46 from both sides:
$86 - 46 = 7x$
$40 = 7x$

Step5: Solve for x

Divide both sides by 7:
$x = \frac{40}{7} \approx 5.7$

Answer:

$x \approx 5.7$