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Problem 24

# In Exercises $24-29$ find the measure of each angle. The ratio of the measures of two complementary angles is $4 : 5 .$

## Discussion

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## Video Transcript

in this question. It says the ratio of measures of two complimentary angles is 4 to 5. The first thing you need to know is that complimentary means two angles too. Angles that adds 90 That ad two 90 degrees. Okay, in this case, are angles are in the ratio of four to find. Any time they give you an algebraic problem of this type, you could sit here and say, OK, the angles could be four and five. Does that ass and 90? No. Okay, multiply by two. So eight in 10 Does that add to 90 No, multiple by three. So 12 and 15 does that add to 90? However, that is very time consuming. So the trick is that you put in ax put in acts with each number in the ratio, so four acts to five X. The reason why is if you look for X over five X is really for five. And now it says the reach of the measures of two complimentary angles and complimentary angles. Add. So four X plus five x is equal to 92 again. We don't want to duel this trial, and ever I would take us quite a while, so nine X is equal to 90. Divide by nine uncle sides and axes equal. It's a 10 at this point. Met. Make sure you answer the question. They wanted to know the each angle. This is fun, the measure of each angle. So take that 10 and plug back in here four times 10 or for multiplied by tennis, 45 multiplied by 10 is 50. So the first angles 40. The 2nd 2nd angle 50 and 40 plus 50 is 90.