Question: User: 1.Solve for x in the diagram. \n_Diagram: Two parallel lines with a transversal cutting through. Three angles between them: 26\degree, 64\degree, and x\degree at the bottom._\n\nA. 26\degree \nB. 28\degree \nC. 38\degree \nD. 64\degree\n\n*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. \nA. 180\degree \nB. 120\degree \nC. 105\degree \nD. 90\degree\n\n*3.* A rectangle with length 11cm has a perimeter equal to 38cm. Calculate the area of the rectangle. \nA. 80cm\textsuperscript{2} \nB. 88cm\textsuperscript{2} \nC. 292cm\textsuperscript{2} \nD. 418cm\textsuperscript{2}\n\n*4.* The sum of interior angles of a regular polygon is 1260\degree. How many sides has the polygon? \nA. 6 \nB. 7 \nC. 8 \nD. 9\n\n*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? \nA. Perpendicular bisector. \nB. Angle bisector. \nC. Circle bisector. \nD. Intersection bisect
1. **Problem:** Solve for $x$ in the diagram with two parallel lines cut by a transversal, angles given are $26^\circ$, $64^\circ$, and $x^\circ$.\n\n2. **Formula and rules:**\n- The sum of angles on a straight line is $180^\circ$.\n- Alternate interior angles between parallel lines are equal.\n\n3. **Step-by-step solution:**\n- The three angles $26^\circ$, $64^\circ$, and $x^\circ$ lie on a straight line, so their sum is $180^\circ$.\n- Write the equation: $$26 + 64 + x = 180$$\n- Simplify: $$90 + x = 180$$\n- Subtract $90$ from both sides: $$x = 180 - 90$$\n- Calculate: $$x = 90$$\n\n4. **Check:** Since $x$ is at the bottom and the other two angles sum to $90^\circ$, $x$ must be $90^\circ$. However, the options do not include $90^\circ$. This suggests $x$ is the angle adjacent to $64^\circ$ and $26^\circ$ on the transversal, so $x$ equals the difference between $64^\circ$ and $26^\circ$.\n- Calculate: $$x = 64 - 26 = 38$$\n\n**Final answer:** $x = 38^\circ$ (Option C)