Question

The measure of angle A is twice that of angle B and one less than that of angle C. If the sum of the measures of the three angles is at least 66, what is the least possible measure of angle A?

Quite hard. :/

Answer 1

17

Answer 2

sry i mean 34

Answer 3

Would you mind if ask for the solution? :)

Answer 4

\[A = 2B\] \[A=C-1\]
Solve for B and C.
\[B=A/2\]
\[C=A+1\]
We know that \[A+B+C = 66\]
Now we substitute:
\[A+(A/2) + (A+1) = 66\]
\[5/2 A + 1 =66\]
\[5/2 A =65\]
\[5A = 130\]
\[A = 26\]
Proof:
\[26 + 13 + 27 = 66\]

Answer 5

Wow. Thank you! :)

Answer 6

Can i ask why it became 5/2?

Answer 7

A + 0.5A + A = 2.5A = (5/2) A

Answer 8

A/2 = 0.5 A

Answer 9

Sorry, easier to explain in decimal form with the limits of displaying fractions here.