contestada

Janelle is building a wooden playhouse, and she needs to cut a board such that it forms angles A and B , where the measure of angle A is 13 of the measure of angle B , and angles A and B are supplementary. What is the measure of angle B ?

Respuesta :

Using the concept of supplementary angles, it is found that the measure of angle B is of 135º.

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  • If two angles are supplementary, the sum of their measures is of 180º.
  • A and B are supplementary, thus:

[tex]A + B = 180[/tex]

  • The measure of angle A is 1/3 of the measure of angle B, thus:

[tex]A = \frac{B}{3}[/tex]

Replacing in the equation for the sum:

[tex]A + B = 180[/tex]

[tex]\frac{B}{3} + B = 180[/tex]

[tex]B + 3B = 540[/tex]

[tex]4B = 540[/tex]

[tex]B = \frac{540}{4}[/tex]

[tex]B = 135[/tex]

The measure of angle B is of 135º.

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