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STEM Excellence Series: Empowering the Next Generation
ANGLE ADDITION POSTULATE
Angle Addition Postulate
Video Examples: Angle Addition Postulate - Geometry Help
Definition Of Angle Addition Postulate
Angle Addition Postulate states that if a point S lies in the interior of ∠PQR, then ∠PQS + ∠SQR = ∠PQR.
More about Angle Addition Postulate
- If the sum of the two angles measure up to 900, then the angles are called to be 'complementary angles'.
- If the sum of the two angles measure up to 1800, then the angles are called to be 'supplementary angles'.
- The angles sharing a common side are called as 'adjacent angles'.
Examples of Angle Addition Postulate
According to angle addition postulate, m∠DAC + m∠CAB = m∠DAB. So, m∠DAB = 350+ 300 = 650.
Video Examples: Angle Addition Postulate - Geometry Help
Solved Example on Angle Addition Postulate
Ques:
Find m∠CAB. [Given ∠DAB = 64° and ∠DAC = 53°.]
Choices:
A. 28
B. 15
C. 11
D. 117
Correct Answer: C
Solution:
Step 1: m∠DAC + m∠CAB = m∠DAB [Angle Addition Postulate.]
Step 2: m∠CAB = m∠DAB - m∠DAC
Step 3: m∠CAB = 64° - 53° [Substitute.]
Step 4: m∠CAB = 11° [Add.]
Quick Summary
- The Angle Addition Postulate allows you to find the measure of a larger angle by adding the measures of its smaller adjacent angles.
- If point S is in the interior of angle PQR, then the measure of angle PQS plus the measure of angle SQR equals the measure of angle PQR.
- Adjacent angles share a common side.
\[ m\angle PQS + m\angle SQR = m\angle PQR \]
🍎 Teacher Insights
Use visual aids and hands-on activities to demonstrate the concept. Emphasize the importance of accurate angle measurement and algebraic manipulation. Provide ample practice problems with varying levels of difficulty.🎓 Prerequisites
- Angles
- Degrees
- Basic Algebra
Check Your Knowledge
Q1: If m∠DAC = 53° and m∠DAB = 64°, find m∠CAB.
Q2: If m∠PQS = 35° and m∠SQR = 30°, find m∠PQR.
Frequently Asked Questions
Q: What are complementary angles?
A: Complementary angles are two angles whose measures add up to 90 degrees.
Q: What are supplementary angles?
A: Supplementary angles are two angles whose measures add up to 180 degrees.