Podcast
Questions and Answers
What is the measure of the supplement of a 65-degree angle?
What is the measure of the supplement of a 65-degree angle?
If the ratio of the lengths of two sides of a triangle is 3:4, what is the length of the longer side if the shorter side is 12 units?
If the ratio of the lengths of two sides of a triangle is 3:4, what is the length of the longer side if the shorter side is 12 units?
How is the upper bound of a measure determined when it is given as 5.2 cm ± 0.3 cm?
How is the upper bound of a measure determined when it is given as 5.2 cm ± 0.3 cm?
What is the value of a complementary angle to a 40-degree angle?
What is the value of a complementary angle to a 40-degree angle?
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If two angles are in the ratio 2:3 and their sum is 90 degrees, what is the measure of the smaller angle?
If two angles are in the ratio 2:3 and their sum is 90 degrees, what is the measure of the smaller angle?
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Study Notes
Supplementary Angles
- The supplement of an angle is the angle that, when added to the original angle, equals 180 degrees.
- Therefore, the supplement of a 65-degree angle is 115 degrees (180 - 65 = 115).
Ratios and Proportions
- A ratio of 3:4 indicates that for every 3 units of the shorter side, there are 4 units of the longer side.
- With a shorter side of 12 units, the longer side is 16 units (12 / 3 * 4 = 16).
Upper Bounds and Measurement Uncertainty
- The upper bound of a measure represents the maximum possible value within a given range of uncertainty.
- The ± 0.3 cm in the measurement 5.2 cm ± 0.3 cm indicates a potential variation of 0.3 cm in either direction.
- Therefore, the upper bound is determined by adding the uncertainty to the measured value (5.2 cm + 0.3 cm = 5.5 cm).
Complementary Angles
- Complementary angles are two angles that add up to 90 degrees.
- The complementary angle to a 40-degree angle is 50 degrees (90 - 40 = 50).
Ratios and Angle Measures
- Two angles in the ratio 2:3 can be represented as 2x and 3x, where x is a common factor.
- Since the sum of the angles is 90 degrees, we have 2x + 3x = 90.
- Solving for x gives us x = 18.
- The smaller angle, represented by 2x, measures 36 degrees (2 * 18 = 36).
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Description
Test your knowledge of angles, triangles, and measurements with this 10th class geometry quiz. Questions cover supplementary and complementary angles, triangle side ratios, and determining upper bounds. Perfect for students preparing for their exams.
