Question

question
in circle $w$, $m\angle zyx = 68^\circ$. solve
for $x$ if $m\overset{\frown}{zx} = (4x + 35)^\circ$. if
necessary, round your answer to the
nearest tenth.
answer
attempt 1 out of 2
$x = $

Explanation:

Step1: Recall inscribed angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. So $m\angle ZYX = \frac{1}{2}m\overset{\frown}{ZX}$

Step2: Substitute given values

Substitute $m\angle ZYX = 68^\circ$ and $m\overset{\frown}{ZX}=(4x+35)^\circ$:
$$68 = \frac{1}{2}(4x + 35)$$

Step3: Multiply both sides by 2

Eliminate the fraction:
$$68 \times 2 = 4x + 35$$
$$136 = 4x + 35$$

Step4: Isolate the term with x

Subtract 35 from both sides:
$$136 - 35 = 4x$$
$$101 = 4x$$

Step5: Solve for x

Divide both sides by 4:
$$x = \frac{101}{4} = 25.25$$

Step6: Round to nearest tenth

Round 25.25 to one decimal place:
$$x \approx 25.3$$

Answer:

$x = 25.3$