contestada

The measure of an angle is 8 degrees less than three times te measure another angle. If the two angles are supplementary, what is the measure of the larger angle?

Respuesta :

iiMGii
Let's solve this problem step-by-step.

First of all, let's establish that supplementary angles are two angles which add up to 180°.
Therefore:

Equation No. 1 -
x + y = 180°

After reading the problem, we can convert it into an equation as displayed as the following:

Equation No. 2 -
3x - 8 + x = 180°

Now let's make (y) the subject in the first equation as it is only possible for (x) to be the subject in the second equation. The working out is displayed below:

Equation No. 1 -
x + y = 180°
y = 180 - x

Then, let's make (x) the subject in the second equation & solve as displayed below:

Equation No. 2 -
3x - 8 + x = 180°
4x = 180 + 8
x = 188 / 4
x = 47°

After that, substitute the value of (x) from the second equation into the first equation to obtain the value of the other angle as displayed below:

y = 180 - x
y = 180 - ( 47 )
y = 133°

We are now able to establish that the value of the two angles are as follows:

x = 47°
y = 133°

In order to determine the measure of the bigger angle, we will need to identify which of the angles is larger.

133 is greater than 47 as displayed below:

133 > 47

Therefore, the measure of the larger angle is 133°.
akposevictor

Given that two angles are supplementary when one of them is 8 degrees less than three times the other, the larger angle is: [tex]\mathbf{133^{\circ}}[/tex]

Recall:

Two angles that are supplementary sum up to 180 degrees.

Given the following:

  • Let x = one of the angles
  • Second angle is: 3x - 8

Since both are supplementary, therefore:

x + (3x - 8) = 180

  • Solve for x

x + 3x - 8 = 180

  • Add like terms

4x - 8 = 180

  • Add 8 to both sides

4x = 180 + 8

4x = 188

  • Divide both sides by 4

x = 47

The smaller angle is [tex]\mathbf{47^{\circ}}[/tex]

The larger angle = 3x - 8

  • Plug in the value of x

[tex]= 3(47) - 8 \\\\\mathbf{= 133^{\circ}}[/tex]

Therefore, given that two angles are supplementary when one of them is 8 degrees less than three times the other, the larger angle is: [tex]\mathbf{133^{\circ}}[/tex]

Learn more here:

https://brainly.com/question/889883

Otras preguntas