Question: IV. Instructions: A. Use the parallelogram POLE at the right to answer each unknown measure. 1. If PL = 20, what is PN? 2. If OL = 12, what is PE? 3. If m\u2220POL = 72\u00b0, what is the m\u2220OPE? 4. If m\u2220ELO = 98\u00b0, what is the m\u2220OPE? 5. If EP = 22, what is OL? B. Find the measures of the unknown value of x and y. 1. 62\u00b0 x y 2. 28 23 x y C. Complete the table. Area of a Parallelogram | Base (b) | Perpendicular Height (h) 1. A = ? | b = 15 cm. | h = 10 cm. 2. A = 320 m\u00b2 | b = 24 m | h = ? 3. A = 176 m\u00b2 | b = 16 m | h = ? parallelogram POLE diagram, position_hint=top-right: P at top-left, O at top-right, L at bottom-right, E at bottom-left, with diagonals PL and EO intersecting at N in the center.

1. **Problem Statement:** Find the unknown measures in parallelogram POLE and solve for x, y, and area values. --- ### Part A: Parallelogram POLE 1. **If $PL = 20$, find $PN$.** - In a parallelogram, diagonals bisect each other. - So, $PN = \frac{PL}{2} = \frac{20}{2} = 10$. 2. **If $OL = 12$, find $PE$.** - Opposite sides of a parallelogram are equal. - So, $PE = OL = 12$. 3. **If $m\angle POL = 72^\circ$, find $m\angle OPE$.** - Adjacent angles between sides and diagonals in parallelogram have special relationships. - $\angle POL$ and $\angle OPE$ are supplementary because $\angle POL$ and $\angle OPE$ are consecutive angles around point $P$ on the diagonal. - So, $m\angle OPE = 180^\circ - 72^\circ = 108^\circ$. 4. **If $m\angle ELO = 98^\circ$, find $m\angle OPE$.** - Opposite angles in parallelogram are equal. - $m\angle ELO = m\angle OPE = 98^\circ$. 5. **If $EP = 22$, find $OL$.** - Opposite sides are equal. - So, $OL = EP = 22$. --- ### Part B: Find $x$ and $y$ in the given angle diagrams **1. Diagram 1:** - Given $62^\circ$, $x$, and $y$ angles around a point. - Assuming $x$ and $y$ are angles on a straight line with $62^\circ$. - Sum of angles on a straight line is $180^\circ$. - So, $62 + x + y = 180$. - Without more info, assume $x = y$ (common in such problems). - Then, $62 + 2x = 180 \Rightarrow 2x = 118 \Rightarrow x = 59$. - So, $y = 59$. **2. Diagram 2:** - Given angles $28$, $23$, $x$, and $y$. - Assuming $x$ and $y$ are supplementary to $28$ and $23$ respectively. - So, $x = 180 - 28 = 152$. - $y = 180 - 23 = 157$. --- ### Part C: Area of Parallelogram Formula: $$A = b \times h$$ where $b$ is base and $h$ is perpendicular height. 1. Given $b = 15$ cm, $h = 10$ cm, find $A$: $$A = 15 \times 10 = 150 \text{ cm}^2$$ 2. Given $A = 320$ m$^2$, $b = 24$ m, find $h$: $$h = \frac{A}{b} = \frac{320}{24} = \frac{320}{\cancel{24}} = \frac{320}{\cancel{24}} = 13.33 \text{ m (approx)}$$ 3. Given $A = 176$ m$^2$, $b = 16$ m, find $h$: $$h = \frac{A}{b} = \frac{176}{16} = 11 \text{ m}$$