Question: 1.Solve for x in the diagram. _Diagram: Two parallel lines with a transversal cutting through. Three angles between them: 26\degree, 64\degree, and x\degree at the bottom._ A. 26\degree B. 28\degree C. 38\degree D. 64\degree *2.* Two interior angles of a hexagon are 120\degree and 180\degree. If the remaining angles are the same, find the measure of each equal angle. A. 180\degree B. 120\degree C. 105\degree D. 90\degree *3.* A rectangle with length 11cm has a perimeter equal to 38cm. Calculate the area of the rectangle. A. 80cm\textsuperscript{2} B. 88cm\textsuperscript{2} C. 292cm\textsuperscript{2} D. 418cm\textsuperscript{2} *4.* The sum of interior angles of a regular polygon is 1260\degree. How many sides has the polygon? A. 6 B. 7 C. 8 D. 9 *5.* A basic school learner decided to draw two intersecting lines and name them OX and OY. She placed a compass at O and drew an arc to intersect OX and OY at A and B respectively. With the compass point at A with a reasonable radius, she drew an arc in the space between XY and repeated same with compass point at B intersecting at C. What is the locus drawn from O through C? A. Perpendicular bisector. B. Angle bisector. C. Circle bisector. D. Intersection bisector.

1. **Problem:** Find $x$ in the diagram with two parallel lines cut by a transversal, angles given are $26^\circ$, $64^\circ$, and $x^\circ$. 2. **Formula and rules:** Angles on a straight line sum to $180^\circ$. Alternate interior angles between parallel lines are equal. 3. **Work:** The three angles $26^\circ$, $64^\circ$, and $x^\circ$ lie on a straight line, so: $$26 + 64 + x = 180$$ $$90 + x = 180$$ $$x = 180 - 90 = 90$$ But $x$ is at the bottom between the parallel lines and transversal, so it is supplementary to $64^\circ$ (alternate interior angles), so $x = 64^\circ$. 4. **Answer:** $x = 64^\circ$ (Option D). --- 1. **Problem:** Two interior angles of a hexagon are $120^\circ$ and $180^\circ$. The remaining four angles are equal. Find each equal angle. 2. **Formula:** Sum of interior angles of a polygon with $n$ sides is: $$S = (n-2) \times 180$$ For hexagon, $n=6$: $$S = (6-2) \times 180 = 4 \times 180 = 720^\circ$$ 3. **Work:** Sum of known angles: $$120 + 180 = 300^\circ$$ Sum of remaining four equal angles: $$720 - 300 = 420^\circ$$ Each equal angle: $$\frac{420}{4} = 105^\circ$$ 4. **Answer:** Each equal angle is $105^\circ$ (Option C). --- 1. **Problem:** Rectangle with length $11$ cm and perimeter $38$ cm. Find area. 2. **Formula:** Perimeter of rectangle: $$P = 2(l + w)$$ Area: $$A = l \times w$$ 3. **Work:** Given $P=38$, $l=11$: $$38 = 2(11 + w)$$ $$\frac{38}{2} = 11 + w$$ $$19 = 11 + w$$ $$w = 19 - 11 = 8$$ Area: $$A = 11 \times 8 = 88$$ 4. **Answer:** Area is $88$ cm\textsuperscript{2} (Option B). --- 1. **Problem:** Sum of interior angles of a regular polygon is $1260^\circ$. Find number of sides. 2. **Formula:** Sum of interior angles: $$S = (n-2) \times 180$$ 3. **Work:** Given $S=1260$: $$1260 = (n-2) \times 180$$ $$\frac{1260}{180} = n - 2$$ $$7 = n - 2$$ $$n = 7 + 2 = 9$$ 4. **Answer:** Polygon has $9$ sides (Option D). --- 1. **Problem:** Two intersecting lines OX and OY with arcs drawn from O intersecting OX and OY at A and B, arcs from A and B intersect at C. Find locus from O through C. 2. **Explanation:** The construction describes the angle bisector method using compass arcs. 3. **Answer:** The locus drawn from O through C is the **angle bisector** (Option B).