1. **Find the value of $x$ given the angles 60°, $x°$, $x°$, $x°$, $x°$.** Since the sum of angles around a point is 360°, we have: $$60 + x + x + x + x = 360$$ $$60 + 4x = 360$$ 2. Subtract 60 from both sides: $$\cancel{60} + 4x = 360 - \cancel{60}$$ $$4x = 300$$ 3. Divide both sides by 4: $$\frac{\cancel{4}x}{\cancel{4}} = \frac{300}{4}$$ $$x = 75$$ --- 4. **Find the indicated measures in parallelogram STUV with diagonals intersecting at W, $VU=123.8$ cm, $TU=108.8$ cm, and $\angle S = 57°$.** Recall properties of parallelograms: - Opposite sides are equal. - Diagonals bisect each other. - Opposite angles are equal. - Adjacent angles are supplementary. (a) $TS$ is opposite to $VU$, so: $$TS = VU = 123.8\text{ cm}$$ (b) $SW$ is half of diagonal $SU$ because diagonals bisect each other. (c) $m\angle SVU$ is equal to $m\angle STU$ because alternate interior angles are equal in parallelograms. (d) $m\angle STU$ is supplementary to $m\angle S$: $$m\angle STU = 180° - 57° = 123°$$ (e) $US$ is opposite to $TV$, so: $$US = TV = 108.8\text{ cm}$$ (f) $m\angle TUV$ is equal to $m\angle SVU$ (opposite angles), so: $$m\angle TUV = 57°$$ --- 5. **Find values of $x$ and $y$ that make the quadrilateral a parallelogram given sides $5x - 4$, $2y + 16$, and $2y + 9$.** For a parallelogram, opposite sides are equal. Set opposite sides equal: $$5x - 4 = 2y + 9$$ $$2y + 16 = \text{other side (not given)}$$ Since only two expressions are given, assume $5x - 4$ and $2y + 9$ are opposite sides. Solve for $x$ and $y$: 1. From: $$5x - 4 = 2y + 9$$ $$5x = 2y + 13$$ 2. Express $y$ in terms of $x$: $$2y = 5x - 13$$ $$y = \frac{5x - 13}{2}$$ Without more info, $x$ and $y$ depend on each other. --- **Final answers:** 1. $x = 75°$ 4a. $TS = 123.8$ cm 4b. $SW = \frac{1}{2} SU$ (exact length depends on $SU$) 4c. $m\angle SVU = 123°$ 4d. $m\angle STU = 123°$ 4e. $US = 108.8$ cm 4f. $m\angle TUV = 57°$ 7. $y = \frac{5x - 13}{2}$ (values depend on additional info)