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SUPPLEMENTARY ANGLES

Supplementary angles are kind of angle pairs whose sum is equal to 180 degrees. This means that when you add the first angle to another angle, its total should equate to exactly 180 degrees.

Here is an example.

A pair angles measuring 30 degrees and 150 degrees respectively. They can be considered as supplementary angles since when 30 degrees is added to 150 degrees, it will result to a total of 180 degrees.

Let us try solving this word problem that involves supplementary angles.

Angle D and angle T are supplementary angles. Find the measure of both angles if the measure of angle D is equal to 3x + 8 and the measure of angle T is equal to 2x - 18.

Here is the solution. Since we are dealing with supplementary angles, we can make an equation that adds the two angles and equates to 180 degrees. With this, the equation formed will be:

Angle D + Angle T = 180

Then, we will be substituting the expressions to each angle. Given that Angle D is equal to 3x + 8 and Angle T is equal to 2x - 18. The equation will become:

(3x + 8) + (2x - 18) = 180

From this equation, we need to find the value of x by doing algebraic manipulations. To do this, first, we need to combine like terms. 3x and 2x are like terms.

3x + 2x + 8 - 18 = 180

5x - 10 = 180

We will then transpose -10 to the other side of the equation to leave the term 5x alone in the left side. Since the sign of the term (-10) that we will transpose is negative, then it will change to its opposite sign, making it +10.

5x = 180 + 10

After this, we will evaluate the sum of 180 and 10, which is 190.

5x = 190

In order to isolate x, we will divide both sides by 5.

5x/5 = 190/5

x = 38

Therefore, the value of x is 38. However, this is not the final answer yet. We still need to substitute this to the two expressions that will give the value of two unknown supplementary angles.

At Angle D:

Angle D = 3x + 8 = 3(38) + 8 = 114 + 8 = 122 degrees

At Angle T:

Angle T = 2x - 18 = 2(38) - 18 = 76 - 18 = 58 degrees

Thus, Angle D measures 122 degrees and Angle T measures 58 degrees.

Types of Angles

1. Acute angles are angles which measure greater than 0 degree but less than 90 degrees.
2. Right angles are angles which measure exactly 90 degrees.
3. Obtuse angles are angles which measure greater than 90 degrees but less than 180 degrees.
4. Straight angles are angles which measure exactly 180 degrees.

Angles inscribed inside a circle have also relationship between their measure and the measure of its intercepted arc. You can read it here: brainly.ph/question/10052201

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