Measure and Sketch Angles - 4th Grade Math

1. Angle XYZ is made up of two adjacent angles measuring $55°$ and $70°$. What is the measure of angle XYZ?
   Answer: $125°$ Angle XYZ measures 125° because 55° + 70° = 125°. Choice A is far too small to represent the sum of both parts. Choice B repeats just one of the two given angles. Choice D overshoots the correct sum by 20°.
2. Lisa is practicing angle measurement and sketching. She measures an angle as $84°$, then sketches an angle that is $96°$. What is the difference between the measures of the two angles?
   Answer: 12° The correct answer is B, 12°, because $96° - 84° = 12°$. Choice A is close but comes from a small subtraction slip. Choice C and Choice D are both larger misses, possibly from misreading one of the two angle measures.
3. One angle measures 70° and another angle measures 95°. If these two angles are placed adjacent to each other, sharing a common ray, what is the measure of the combined angle?
   Answer: 165° The combined angle measures 165° because 70° + 95° = 165°. Choice A is 10° too low. Choice C is 10° too high. Choice D adds 20° too much to the actual sum.
4. When using a protractor to measure the angle in the figure, which statement best describes the correct measurement process?
   Answer: Place the center point on the vertex, align one ray with zero, and read where the second ray crosses the same scale The correct process requires placing the protractor's center point on the vertex, aligning one ray with the zero mark, and reading where the second ray crosses the same scale you started from. Choice A ignores proper alignment and scale consistency. Choice C places the center incorrectly. Choice D describes an invalid measurement technique.
5. Look at the protractor measurement shown below. Carlos needs to sketch an angle that is $25°$ less than twice the measured angle. What should be the measure of Carlos's angle?
   Answer: $155°$ The protractor shows an angle measuring $90°$. Twice this angle is $90° × 2 = 180°$. An angle that is $25°$ less than this would be $180° - 25° = 155°$. Choice A incorrectly calculates $90° × 2 - 45°$. Choice B incorrectly calculates $90° × 2 - 35°$. Choice D incorrectly calculates $90° × 2 - 15°$.
6. Maya measures an angle with a protractor and finds it is $72°$. What is the measure of an angle that is $18°$ larger than the one she measured?
   Answer: 90° The correct answer is B, 90°, because 72° plus 18° equals 90°. Choice A, 54°, comes from subtracting instead of adding. Choices C and D come from addition errors.
7. Examine the angle shown in the diagram below. Lisa wants to divide this angle into three equal parts. What would be the measure of each smaller angle?
   Answer: $40°$ The angle shown measures $120°$. Dividing this into three equal parts: $120° ÷ 3 = 40°$. Choice A incorrectly calculates $105° ÷ 3$. Choice C incorrectly calculates $135° ÷ 3$. Choice D incorrectly calculates $150° ÷ 3$.

Start this quiz