Differences Between Complementary and Supplementary Angles

The primary distinction between a complementary angle and a supplementary angle is that the sum of the two angles that comprise a complementary angle is 90°, but the total of the two angles that comprise a supplementary angle is 180°.

Complementary angles are generated when the total of two angles equals precisely 90°. When two complementary angles are adjacent, a right angle is created. For instance, two angles measuring 65° and 25° are complementary since their sum is exactly 90°.

When the total of two angles equals exactly 180°, they are referred to as supplementary angles. By combining complementary angles together, right angles can be produced. For instance, if two angles measure 110° and 70°, they can be considered complementary angles because their sum equals 180°.

Definition of angles 

Angles are created when two lines meet at a single point. An ‘angle’ is the measurement of the ‘opening’ between these two rays. It is denoted with the sign . Typically, angles are measured in degrees and radians, a unit of circularity or rotation. Angles are an integral component of our daily lives. Engineers and architects employ angles while designing highways, buildings, and athletic facilities.

Types of Angles

Six sorts of angles exist. On the basis of angle measurement, each type of angle has a distinct identifier. Let us read about each sort of angle and its attributes separately.

Acute Angle

Acute angles have a measure greater than 0° and less than 90°.

Right angle

When an angle is 90°, it is referred to as a right angle. Because it resembles the letter L, a right angle is instantly identifiable.

Obtuse Angle

When an angle’s measurement is less than 180° but greater than 90°, it is obtuse.

Straight-angle

A straight angle refers to the angle formed by a straight line. In other words, a right angle is a straight line, and the angle generated by two rays equals 180°. At a right angle, the two beams are perpendicular to one another. A straight angle consists of two right angles. Since a right angle has a measure of 180°, it is half of a complete revolution of a circle.

Reflex Angle

A reflex angle has a measure of more than 180°  but less than 360°.

Complete angle

When the measurement of an angle equals 360°, the angle is considered complete.

Definition of Complementary and Supplementary Angles

Two angles are considered complementary if their sum is equal to 90°, or a right angle. These angles are considered complementary to one another. Again, the two angles need not be contiguous in this instance. Nevertheless, their aggregate must equal 90°. Putting this into an equation, if C and D are two angles, then C plus D equals 90°.

Two angles are referred to as supplementary angles if their sum equals 180°. Consequently, the complementary angles are referred to as complementary. It is not necessary for the two angles to be contiguous; their aggregate must equal 180°. Putting this into an equation, if A and B are two angles, then A + B = 180°.

Complementary angle theorem

According to the complementary angle theorem, if two angles are complementary to the same angle, they are congruent.

Supplementary angle theorem 

According to the supplementary angle theorem, if two angles are supplementary to the same angle, then the two angles are congruent.

Real-Life Examples of Complementary and Supplementary Angles

When a rectangular loaf of bread is split into two pieces along the diagonal, the resulting shapes are two right triangles with complementary angles. When the minute hand is at 12 o’clock and the hour hand is at three o’clock, a complementary angle is formed.

Supplementary angles are formed when the sum of two angles equals 180°. Examples of extra angles in the actual world include stars, cups, and logos.

Tricks for Complementary and Supplementary Angles

The letter ‘C’ stands for both ‘complementary’ and ‘corner. Consequently, when two complementary angles combine, they produce a ‘corner (right)’ angle.

The letter ‘S’ stands for supplementary and straight. Consequently, when two supplementary angles are joined, they create a ‘straight’ angle.

Similar to how 90° precedes 180°, the letter ‘C’ in complimentary comes before the letter ‘S’ in supplemental.

Conclusion 

Complementary angles are generated when the sum of two angles equals precisely 90°. When two complementary angles are adjacent, a right angle is created. Angles are created when two lines meet at a single point – an ‘angle’ is the measurement of the opening between these two rays. Two angles are considered complementary if their sum is equal to 90°, or a right angle. Two angles are referred to as ‘Supplemental’ if their aggregate equals 180°. Examples of extra angles in the actual world include stars, cups, and logos.