Question 251906: If the measures of the angles of a triangle are in the ratio 1:3:5, the number of degrees in the measure of the smallest angle is...
a. 10
b. 20
c. 60
d. 180
pllz help me!!
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
I have no idea why I should help someone who is too lazy to spell out the word 'please,' but here goes anyway.
If the ratio of the three angles is 1:3:5, then the smallest angle is 1 part, the next larger angle is 3 parts, and the largest angle is 5 parts for a total of 1 plus 3 plus 5 equals 9 parts. The sum of the angles of a triangle is always 180 degrees. Dividing 180 by 9 means that 1 part is 20 degrees. Since the smallest angle is 1 part, the smallest angle must be 20 degrees.
To check the answer, consider that the middle-sized angle is 3 parts, or 3 times 20 = 60 degrees, and the largest angle is 5 parts or 5 times 20 = 100 degrees, and then 20 + 60 + 100 = 180 -- so the answer checks.
John
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