Question: ACTIVITY for AUGUST 6, 2026 I. Drawing in Geometry: Copy $\angle ABC$. Draw $CB$ and $AB$. Label a point $D$ so that $B$ is between $A$ and $D$. Label a point $E$ so that $B$ is between $C$ and $E$. Graph/shape: In the upper-right center there is a small angle diagram with point $A$ on the left, point $B$ on the right, and point $C$ above-left; one ray goes from $B$ to $A$ horizontally left, and another ray goes from $B$ to $C$ diagonally up-left. II. Refer to the figure below for #1 to 4. 1) Name the vertical angle to: a) $\angle 1$ b) $\angle 2$ c) $\angle 3$ d) $\angle 4$ 2) Name 2 angles linear pair with: a) $\angle 1$ b) $\angle 4$ c) $\angle 6$ d) $\angle 7$ 3) If the $m\angle 2 = 87^\circ$, find the measures of $\angle 1$, $\angle 7$, and $\angle 8$. 4) If the $m\angle 4 = 105^\circ$, find the measures of $\angle 3$, $\angle 5$, and $\angle 6$. Graph/shape: In the lower-right center there is a boxed geometry figure with two slanted lines labeled $l$ and $m$ intersecting a horizontal line, plus a label $n$ near the right side; angles around the left intersection are 1, 2, 7, 8 and around the right intersection are 3, 4, 5, 6. NOTE: - Copy and answer on a short bond paper. - To be submitted tomorrow, August 7, 2026.answer this please

1. **State the problem:** We are given a geometry figure with angles labeled 1 to 8 formed by two intersecting lines and a transversal. We need to find vertical angles, linear pairs, and calculate angle measures given some values. 2. **Vertical angles:** Vertical angles are pairs of opposite angles formed by two intersecting lines. They are equal in measure. 3. **Linear pairs:** Linear pairs are adjacent angles formed when two lines intersect. Their measures add up to $180^\circ$. --- **1) Name the vertical angle to:** - a) $\angle 1$ is vertical to $\angle 3$. - b) $\angle 2$ is vertical to $\angle 4$. - c) $\angle 3$ is vertical to $\angle 1$. - d) $\angle 4$ is vertical to $\angle 2$. --- **2) Name 2 angles linear pair with:** - a) $\angle 1$ forms linear pairs with $\angle 2$ and $\angle 7$. - b) $\angle 4$ forms linear pairs with $\angle 3$ and $\angle 5$. - c) $\angle 6$ forms linear pairs with $\angle 5$ and $\angle 8$. - d) $\angle 7$ forms linear pairs with $\angle 1$ and $\angle 8$. --- **3) Given $m\angle 2 = 87^\circ$, find $m\angle 1$, $m\angle 7$, and $m\angle 8$:** - Since $\angle 1$ and $\angle 2$ are linear pairs: $$m\angle 1 + m\angle 2 = 180^\circ$$ $$m\angle 1 = 180^\circ - 87^\circ = 93^\circ$$ - $\angle 1$ and $\angle 7$ are vertical angles, so: $$m\angle 7 = m\angle 1 = 93^\circ$$ - $\angle 7$ and $\angle 8$ are linear pairs: $$m\angle 7 + m\angle 8 = 180^\circ$$ $$m\angle 8 = 180^\circ - 93^\circ = 87^\circ$$ --- **4) Given $m\angle 4 = 105^\circ$, find $m\angle 3$, $m\angle 5$, and $m\angle 6$:** - $\angle 3$ and $\angle 4$ are vertical angles: $$m\angle 3 = m\angle 4 = 105^\circ$$ - $\angle 4$ and $\angle 5$ are linear pairs: $$m\angle 4 + m\angle 5 = 180^\circ$$ $$m\angle 5 = 180^\circ - 105^\circ = 75^\circ$$ - $\angle 5$ and $\angle 6$ are vertical angles: $$m\angle 6 = m\angle 5 = 75^\circ$$ --- **Final answers:** - Vertical angles: - $\angle 1 \leftrightarrow \angle 3$ - $\angle 2 \leftrightarrow \angle 4$ - Linear pairs: - $\angle 1$ with $\angle 2$, $\angle 7$ - $\angle 4$ with $\angle 3$, $\angle 5$ - $\angle 6$ with $\angle 5$, $\angle 8$ - $\angle 7$ with $\angle 1$, $\angle 8$ - Measures: - $m\angle 1 = 93^\circ$ - $m\angle 7 = 93^\circ$ - $m\angle 8 = 87^\circ$ - $m\angle 3 = 105^\circ$ - $m\angle 5 = 75^\circ$ - $m\angle 6 = 75^\circ$