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Calculate Acute Angle a and Reflex Angle b Using a Protractor
Mathematics
Grade 7 (Junior High School)
Question Content
a) What is the size of angle a? b) Use your answer to part a) to work out the size of reflex angle b. Give your answers to the nearest degree. (A protractor diagram shows angle a between a horizontal line and an upward ray, and reflex angle b is the larger angle around the same vertex with the same sides.)
Correct Answer
a) 70°; b) 290°
Detailed Solution Steps
1
Step 1: Measure angle a using the protractor. The ray aligns with the 70° mark on the protractor, so angle a = 70° (to the nearest degree).
2
Step 2: Recall that a full circle is 360°. A reflex angle is the larger angle formed by two lines, so to find reflex angle b, subtract the measure of angle a from 360°.
3
Step 3: Calculate reflex angle b: 360° - 70° = 290°.
Knowledge Points Involved
1
Protractor Use for Angle Measurement
A protractor is a tool used to measure angles in degrees. To measure an acute or obtuse angle, align one side of the angle with the 0° mark of the protractor, then read the degree mark where the other side intersects the protractor. This is used for measuring angles like angle a in the problem.
2
Reflex Angle Definition
A reflex angle is an angle that measures greater than 180° but less than 360°. It is the larger angle formed when two lines intersect, opposite to the smaller acute, right, or obtuse angle between the same lines.
3
Full Circle Angle Sum
A full circular rotation equals 360°. This fact is used to calculate reflex angles by subtracting the smaller angle between two lines from 360°, as the sum of the smaller angle and its corresponding reflex angle is always 360°.
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