On a clock, there are 12 hour markers dividing the circle into 12 equal parts. From 12 to 3 spans 3 of these parts, so the fraction is 3/12 = 1/4. This represents 90° or 1/4 of the full circle. Choice B is correct. Choice A would span 4 hour markers. Choice C would span 2 hour markers. Choice D would span 1 hour marker.

The first angle is 2/9 × 360° = 80°. The second angle is 60°. The difference is 80° - 60° = 20°, so the first angle is 20° larger. Choice A is correct. Choice B reverses the comparison. Choice C uses 40° instead of 20°. Choice D both reverses the comparison and uses 40°.

If the angle contains 72 one-degree angles, it measures 72°. Since a full circle is 360°, the fraction is 72/360 = 1/5. Choice B is correct. Choice A represents 90° (360 ÷ 4). Choice C represents 60° (360 ÷ 6). Choice D represents 80° (2 × 360 ÷ 9).

When you see a question about spinners and angles, you're working with the relationship between degrees and equal parts of a circle. A complete circle has 360 degrees, so you need to figure out how those degrees are divided among the sections.

The key information tells you that 144 degrees covers exactly 2 sections. This means each section takes up $$144 \div 2 = 72$$ degrees. Now you can find the total number of sections by dividing the complete circle by the size of each section: $$360 \div 72 = 5$$ sections.

Let's check why the other answers don't work. Answer A (8 sections) would mean each section is $$360 \div 8 = 45$$ degrees, so 2 sections would only be 90 degrees, not 144. Answer B (6 sections) would make each section $$360 \div 6 = 60$$ degrees, so 2 sections would be 120 degrees, still too small. Answer D (10 sections) would create sections of $$360 \div 10 = 36$$ degrees each, making 2 sections only 72 degrees, which is way too small.

Only answer C (5 sections) gives you the correct relationship where 2 sections equal exactly 144 degrees.

Remember this strategy: when a spinner question gives you an angle and the number of sections it covers, divide to find the size of one section, then divide 360 by that amount to find the total sections. This two-step approach will help you solve any similar spinner problem.

When working with angles and circles, remember that a complete circle contains 360 one-degree angles (360°). This question asks you to work with fractions of a circle and calculate angle differences.

Tommy's current angle contains 40 one-degree angles, so his angle measures 40°. To express this as a fraction of the circle, you divide by the total degrees in a circle: $$\frac{40}{360} = \frac{1}{9}$$ of the circle.

The teacher wants Tommy to make his angle equal to $$\frac{1}{6}$$ of the circle. To find how many degrees this represents, multiply: $$\frac{1}{6} \times 360° = 60°$$. Since Tommy currently has 40°, he needs $$60° - 40° = 20°$$ more, which means 20 more one-degree angles.

Looking at the wrong answers: Choice A (30 more angles) would give Tommy $$40° + 30° = 70°$$, which is too much. Choice B (25 more angles) would result in $$40° + 25° = 65°$$, still too much. Choice D (35 more angles) would create $$40° + 35° = 75°$$, which is way too large for $$\frac{1}{6}$$ of a circle.

The correct answer is C: 20 more angles.

Study tip: When working with circle fractions, always convert to degrees first by multiplying the fraction by 360°. This makes the arithmetic much clearer than trying to work directly with fractions.

When you see a problem about angles and fractions of circles, remember that a complete circle always measures 360 degrees. Your job is to find what fraction each angle represents, convert those to degrees, then compare them.

Let's work through this step by step. The first angle has an arc that is $$\frac{1}{4}$$ of the circle, so: $$\frac{1}{4} \times 360° = 90°$$. The second angle has an arc that is $$\frac{1}{6}$$ of the circle, so: $$\frac{1}{6} \times 360° = 60°$$. To find how many more degrees the first angle has than the second, subtract: $$90° - 60° = 30°$$.

Now let's see why the other answers don't work. Choice A (90 degrees) gives you just the measure of the first angle—you forgot to subtract the second angle. Choice B (45 degrees) might come from incorrectly thinking $$\frac{1}{4}$$ of 360 is 45, or from making an error in your fraction calculations. Choice C (60 degrees) gives you just the measure of the second angle—again, you forgot the subtraction step.

The correct answer is D (30 degrees).

Remember this pattern: when comparing angles as fractions of a circle, first convert each fraction to degrees by multiplying by 360, then perform the operation the problem asks for. Don't stop after finding just one angle's measure—make sure you complete all the steps the question requires.

This question tests 4th grade understanding that an angle is measured with reference to a circle, where a one-degree angle turns through 1/360 of a circle (CCSS.4.MD.5.a). Angles are measured by considering a circle with its center at the vertex (common endpoint of the rays). The angle measure is determined by the fraction of the circular arc between where the two rays intersect the circle. A full circle is 360 degrees, so a one-degree angle (1°) turns through 1/360 of the circle, and any angle can be measured by counting how many one-degree angles it contains. A full circle represents 360° of rotation. Choice C is correct because full circle = 360°. Choice A represents using 100 instead of 360 (percentage confusion), which happens when students think of percentages (100) instead of degrees (360). To help students: Use a circular model (like a clock or pizza) to show that a full circle has 360°. Emphasize the definition: a one-degree angle (1°) is 1/360 of a circle—this is why we have 360° in a full circle. Show benchmark fractions: 1/2 circle = 180°, 1/4 circle = 90°, 1/8 circle = 45°. Draw circles with rays from center to edge, shading the arc between rays to visualize the fraction. Use clock faces: 12 hours on a clock, so each hour = 1/12 circle = 30°. Watch for: students who think 1° = 1/100 (percentage confusion), students who confuse 180° (half circle) with 360° (full circle), and students who don't connect the fraction of the circle to the angle measure.

This question tests 4th grade understanding that an angle is measured with reference to a circle, where a one-degree angle turns through 1/360 of a circle (CCSS.4.MD.5.a). Angles are measured by considering a circle with its center at the vertex (common endpoint of the rays). The angle measure is determined by the fraction of the circular arc between where the two rays intersect the circle. A full circle is 360 degrees, so a one-degree angle (1°) turns through 1/360 of the circle, and any angle can be measured by counting how many one-degree angles it contains. An angle that is 1/12 of the circle corresponds to (1/12) × 360° = 30°. Choice B is correct because 1/12 × 360° = 30°, demonstrating understanding that angle measure is fundamentally defined by the fraction of a circle through which the angle turns. Choice A represents inverting the fraction (12°), which happens when students miscalculate the fraction-degree conversion. To help students: Use a circular model (like a clock or pizza) to show that a full circle has 360°. Emphasize the definition: a one-degree angle (1°) is 1/360 of a circle—this is why we have 360° in a full circle. Show benchmark fractions: 1/2 circle = 180°, 1/4 circle = 90°, 1/8 circle = 45°. Draw circles with rays from center to edge, shading the arc between rays to visualize the fraction. Use clock faces: 12 hours on a clock, so each hour = 1/12 circle = 30°. Watch for: students who think 1° = 1/100 (percentage confusion), students who confuse 180° (half circle) with 360° (full circle), and students who don't connect the fraction of the circle to the angle measure.

This question tests 4th grade understanding that an angle is measured with reference to a circle, where a one-degree angle turns through 1/360 of a circle (CCSS.4.MD.5.a). Angles are measured by considering a circle with its center at the vertex (common endpoint of the rays). The angle measure is determined by the fraction of the circular arc between where the two rays intersect the circle. A full circle is 360 degrees, so a one-degree angle (1°) turns through 1/360 of the circle, and any angle can be measured by counting how many one-degree angles it contains. An angle that is 1/2 of the circle corresponds to 1/2 × 360° = 180°. Choice C is correct because 1/2 × 360° = 180°, which demonstrates understanding that angle measure is fundamentally defined by the fraction of a circle through which the angle turns. Choice A represents using 1/4 instead of 1/2 (90°), which happens when students confuse half with quarter or miscalculate the fraction. To help students: Use a circular model (like a clock or pizza) to show that a full circle has 360°. Emphasize the definition: a one-degree angle (1°) is 1/360 of a circle—this is why we have 360° in a full circle. Show benchmark fractions: 1/2 circle = 180°, 1/4 circle = 90°, 1/8 circle = 45°. Draw circles with rays from center to edge, shading the arc between rays to visualize the fraction. Use clock faces: 12 hours on a clock, so each hour = 1/12 circle = 30°. Watch for: students who think 1° = 1/100 (percentage confusion), students who confuse 180° (half circle) with 360° (full circle), and students who don't connect the fraction of the circle to the angle measure.

This question tests 4th grade understanding that an angle is measured with reference to a circle, where a one-degree angle turns through 1/360 of a circle (CCSS.4.MD.5.a). Angles are measured by considering a circle with its center at the vertex (common endpoint of the rays). The angle measure is determined by the fraction of the circular arc between where the two rays intersect the circle. A full circle is 360 degrees, so a one-degree angle (1°) turns through 1/360 of the circle, and any angle can be measured by counting how many one-degree angles it contains. A one-degree angle represents 1/360 of a complete rotation. Choice B is correct because 1° = 1/360 by definition. Choice D represents using 1/100 instead of 1/360 (percentage confusion), which happens when students think of percentages (100) instead of degrees (360). To help students: Use a circular model (like a clock or pizza) to show that a full circle has 360°. Emphasize the definition: a one-degree angle (1°) is 1/360 of a circle—this is why we have 360° in a full circle. Show benchmark fractions: 1/2 circle = 180°, 1/4 circle = 90°, 1/8 circle = 45°. Draw circles with rays from center to edge, shading the arc between rays to visualize the fraction. Use clock faces: 12 hours on a clock, so each hour = 1/12 circle = 30°. Watch for: students who think 1° = 1/100 (percentage confusion), students who confuse 180° (half circle) with 360° (full circle), and students who don't connect the fraction of the circle to the angle measure.