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Two supplementry angles are in the ratio of 5:7 . find the measure of the angles

Sagot :

Answer:

75 degrees and 105 degrees

Step-by-step explanation:

Supplementary angles are those angles that sum up to 180 degrees

So angle A + B = 180 or B = 180 - A

then A/B = 5/7

7A = 5B

7A = 5(180 - A)

7A = 900 - 5A

12A = 900

A = 75

then B = 180 - A = 180 - 75 = 105

Let the the two given supplementary angles be A & B respectively. Ratio of angle A to the ratio of angle B is 5/7. And we've been asked to find out the measure of angle A & B.

As we know that supplementary angle are the ones which have the sum of angles and tend to 180°. Thus we can write by forming equation that,

[tex]:\implies\rm{a + b = 180 \: ...(1)}[/tex]

[tex]:\implies\rm{b = 180 - a \: ...(2)}[/tex]

Now as per the given ratio we can write,

[tex]:\implies\rm{ \frac{a}{b} = \frac{5}{7} }[/tex]

[tex]:\implies\rm{7a = 5b}[/tex]

[tex]:\implies\rm{7a = 5(180 - a) \: ...(from \: 2)}[/tex]

[tex]:\implies\rm{7a = 900 - 5a}[/tex]

[tex]:\implies\rm{7a + 5a = 900}[/tex]

[tex]:\implies\rm{12a = 900}[/tex]

[tex]:\implies\rm{a = \frac{900}{12} }[/tex]

[tex]:\implies\rm{a = 75}[/tex]

Now by equation (2) we can write,

[tex]:\implies\rm{b = 180 - a \: ...(from \: 2)}[/tex]

[tex]:\implies\rm{b = 180 - 75}[/tex]

[tex]:\implies\rm{b = 105}[/tex]

  • The measure of angles are 75° and 105°.

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