Question

a) determine the measure of angle x in the shape below. assume c is the center of the circle. (4 marks)

recall: inscribed angle theorem: the measure of the central angle is twice the measure of an inscribed angle. solve for x using 2x = y.

the measure of angle x is ______.

b) the regular polygon below has 15 equal sides. find the measure of angle x. (4 marks)

recall: sum of interior angles of polygons formula: (n - 2) * 180 degrees, where n represents the number of sides.

the measure of angle x is ______.

Explanation:

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<reasoning>

Question a: Apply the Inscribed Angle Theorem

\[

$$\begin{aligned} &y = 49^\circ \\ &2x = y \implies 2x = 49^\circ \\ &x = \frac{49^\circ}{2} = 24.5^\circ \end{aligned}$$

\]

Question b: Calculate the interior angle of a 15-sided regular polygon

\[

$$\begin{aligned} &n = 15 \\ &S = (15 - 2) \times 180^\circ = 13 \times 180^\circ = 2340^\circ \\ &x = \frac{2340^\circ}{15} = 156^\circ \end{aligned}$$

\]
</reasoning>

<answer>

Question a

The measure of angle x is <blank>\(24.5^\circ\)</blank>.

Question b

The measure of angle x is <blank>\(156^\circ\)</blank>.
</answer>

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"Mathematics",
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"Inscribed Angles and Polygon Interior Angles"
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Answer:

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<reasoning>

Question a: Apply the Inscribed Angle Theorem

\[

$$\begin{aligned} &y = 49^\circ \\ &2x = y \implies 2x = 49^\circ \\ &x = \frac{49^\circ}{2} = 24.5^\circ \end{aligned}$$

\]

Question b: Calculate the interior angle of a 15-sided regular polygon

\[

$$\begin{aligned} &n = 15 \\ &S = (15 - 2) \times 180^\circ = 13 \times 180^\circ = 2340^\circ \\ &x = \frac{2340^\circ}{15} = 156^\circ \end{aligned}$$

\]
</reasoning>

<answer>

Question a

The measure of angle x is <blank>\(24.5^\circ\)</blank>.

Question b

The measure of angle x is <blank>\(156^\circ\)</blank>.
</answer>

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