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?

Answer 1

Need the solution. :)

Answer 2

Wanna learn how to do it or just the answer?

Answer 3

i wanna learn how to do it. :) please?

Answer 4

Sure, you'll need a pen and a paper to make it simpler for you tho :)

Answer 5

okay. :) then?

Answer 6

First off.. all those kinds of mathematical problems have one huuuuge key to them : you have to be able to translate those words into mathematical sentences (ie: with numbers)

Answer 7

1st, draw a square... and name 3 corners : A, B and C... it'll help visualize the problem beofre we attempt it

Answer 8

Basically we want to know how to represent the values of A, B and C... once that's done, the rest unfolds

Answer 9

To start, we'll name the first corner A, and make it the value X and go from there...

Answer 10

so...
A = x

Answer 11

Can you tell me what we know about B?

Answer 12

A = 2B
A = C-1
2B = C - 1
C-2B = 1
A + B + C is at least 66?

Answer 13

how will i know the value of a b and c?

Answer 14

still there?

Answer 15

yes, still here, i think my internet froze for a sec

Answer 16

Hmm... Can you explain to me your 2B = C-1?

Answer 17

i think the value of a is c-1

Answer 18

Well I'm realizing I have one way to solve this, using an equiation with "x" as a variable... But is that the way you,re supposed to use too?

Answer 19

Like... I'd made an equation using the \[\ge\] symbol

Answer 20

Like... I'd try to describe all my angles...

I know that A is twice the value of B... so... if we say
B = x degrees
then
A = 2x degrees

makes sense?

Answer 21

Then you do on the square you drew you write "x" inside the corner of B to mark it as it's value... and write "2x" in A's corner to mark it's value

Answer 22

okay. got it. then? :)

Answer 23

So far we have...
B = x
A = 2x
C = ?

Let's find C! What do we know of C? ... well we know that the measure of A is one less than that of angle C... How would you write that mathematically?

Answer 24

Do you know what I mean by "write that mathematically"?

Answer 25

A =C-1 right?

Answer 26

or C=2x-1

Answer 27

Hmm, incorrect... read the sentence again ;) gotta be careful!

"A is one less than C"...

Answer 28

C=1-2x?

Answer 29

hello? :)

Answer 30

It's kind of counter intuitive... that's why you have to be careful...

If they say A is one less than C...

A = 2x <--- this is LESS than C... so C is one more than A... how do you write "one more" in math? ... +1!
C is actually A+1

Answer 31

"A is one less than C" can also be read "C is one more than A". Do you agree that it means the same thing? It makes the understanding simpler... And avoids small mistakes like that

Answer 32

Makes sense?

Answer 33

okaaay. So
B=x
A=2x
and C= 2x+1 :)

Answer 34

yap.

Answer 35

Yep yep!

Now that we have this... rest is just putting it together... Whats the last part of the question? How do you put "the sum of the measures of the three angles is at least 66" in a math sentence?

Answer 36

all right then? :)

Answer 37

Well tell me? How do you write "the sum of the measures of the three angles is at least 66"? This will be our equation to solve

Answer 38

oooh. thanks for that! :) all's clear.

Answer 39

Cool... so what is the answer?

Answer 40

\[x+2x+2x+1\ge66?\]

Answer 41

hot stuff :) so what is x?

Answer 42

oooh. thanks for that! :) all's clear.

Answer 43

13?

Answer 44

oooh. thanks for that! :) all's clear.

Answer 45

is it right?

Answer 46

Good, although an exact answer would be \[x \ge 13\]
Sometimes teachers can be picky with stuff like that... :P

Answer 47

you've solved the equation, but not the problem yet... What is the question asked in the problem?

Answer 48

oooh. thanks for that! :) all's clear.

Answer 49

thaaanks! Got that already. I just need to substitute it right?

Answer 50

Yep... Just be careful cuz when i solved it quickly at 1st I was gonna answer "at least 13", but that wouldn,t be correct... since we have to substitute in A, and A=2x...

A= 2x and x larger or equal as 13
so
\[A \ge2*13\]
\[A \ge26\]

Answer 51

oooh. thanks for that! :) all's clear.

Answer 52

so the answers are 13, 26, and 17?

Answer 53

Well those are the minimal values yes... but the actual question is "what is the least possible measure of angle A?"

Answer 54

to which the answer is 26 ;)

Answer 55

Good work! hihihi

Answer 56

Best advice I could give you is to split the question is different pieces and make sure you understand it 100%, you seem to read it too quickly and might lose points in an exam for answering the wrong question or something ;)

Answer 57

oooh. thanks for that! :) all's clear.

Answer 58

thanks!

Answer 59

My pleasure!

Alright, take care! :)