1. Problem: One angle of a triangle is 70°. The other two angles are in the ratio 3:2. Find the measure of the other two angles. Step 1: Let the other two angles be $3x$ and $2x$. Step 2: Sum of angles in a triangle is $180^\circ$. Step 3: Write equation: $70 + 3x + 2x = 180$. Step 4: Simplify: $5x = 110 \Rightarrow x = 22$. Step 5: Find angles: $3x = 66^\circ$, $2x = 44^\circ$. Answer: (c) 66°, 44°. 2. Problem: Identify the equilateral triangle among (a) ACE, (b) BCE, (c) CBD, (d) ABD. Step 1: Equilateral triangle has all sides equal. Step 2: From figure, triangle ACE has all sides equal. Answer: (a) ACE. 3. Problem: Find measure of angle ∠ADB if AB is a straight line. Step 1: Straight line angle is $180^\circ$. Step 2: Given angles and figure show ∠ADB = $115^\circ$. Answer: (b) 115°. 4. Problem: Find measure of angle ∠CAB. Step 1: From figure and given data, ∠CAB = $50^\circ$. Answer: (b) 50°. 5. Problem: Identify an angle of quadrilateral AFCB among ∠1, ∠2, ∠3, ∠4. Step 1: Quadrilateral angles are at vertices A, F, C, B. Step 2: From figure, ∠3 is an angle of AFCB. Answer: (c) ∠3. 6. Problem: Find ∠BFC if ∠FBC = ∠FCB = 75°. Step 1: Triangle BFC has angles summing to $180^\circ$. Step 2: Calculate ∠BFC = $180 - 75 - 75 = 30^\circ$. Answer: (d) 30°. 7. Problem: Identify a sector of the circle with center O among (a) ACB, (b) BC, (c) COB, (d) AO. Step 1: A sector is area bounded by two radii and an arc. Step 2: Segment COB is bounded by radii OC and OB and arc CB. Answer: (c) COB. 8. Problem: Which statement is true? (a) Chord AC is bigger than chord BC. (b) The biggest chord of the circle is double the length of OC. (c) AB = 2AC. (d) OC and CB are radii. Step 1: OC and CB are radii as they connect center O to circumference. Step 2: The biggest chord is diameter, which is double radius OC. Step 3: Chord AC and BC lengths depend on figure; cannot confirm (a) or (c) without data. Answer: (b) and (d) are true; since only one choice allowed, (d) OC and CB are radii. 9. Problem: Count rectangles and squares in figure 1. Step 1: Given options: 4, 16, 20, 36. Step 2: Counting all rectangles and squares formed by grid lines yields 36. Answer: (d) 36. 10. Problem: Count rectangles and squares in figure 2. Step 1: Given options: 4, 6, 8, 12. Step 2: Counting all quadrilaterals formed yields 8. Answer: (c) 8. Summary: 1. (c) 66°, 44° 2. (a) ACE 3. (b) 115° 4. (b) 50° 5. (c) ∠3 6. (d) 30° 7. (c) COB 8. (d) OC and CB are radii 9. (d) 36 10. (c) 8