PREVIOUSLY ASKED IN:
CTET 2026
Answer
\( 72^{\circ} \)
Explanation
The sum of two supplementary angles is always \( 180^{\circ} \). Therefore, \( (3x - 30) + (2x + 20) = 180 \) \( \Rightarrow 5x - 10 = 180 \) \( \Rightarrow 5x = 190 \) \( \Rightarrow x = 38 \). We need to find the value of \( (2x - 4^{\circ}) \). Substituting \( x \), we get \( 2(38) - 4 = 76 - 4 = 72^{\circ} \).
Key Points
- > Supplementary Angles: Two angles whose sum is 180 degrees.
- > Complementary Angles: Two angles whose sum is 90 degrees.
- > Angles on a straight line always sum up to 180 degrees.
- > While solving equations, group the variables on one side and constants on the other.
- > Read the question carefully as it doesn't ask for just \( x \) but an expression involving \( x \).
- > Degree (°) is the standard unit of angle measurement in elementary geometry.
Additional Information
Types of Angles
| Angle Name | Measurement | Property |
|---|---|---|
| Acute Angle | 0° < θ < 90° | Smaller than a right angle |
| Right Angle | 90° | Formed by perpendicular lines |
| Obtuse Angle | 90° < θ < 180° | Larger than 90°, smaller than 180° |
| Reflex Angle | 180° < θ < 360° | Larger than a straight angle |
Memory Tips
- S for Straight: Supplementary angles form a Straight line (180°).
- C for Corner: Complementary angles form a Corner (90°).