Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Our platform offers a seamless experience for finding reliable answers from a network of experienced professionals. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
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°.
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.
