Question

The measures of the three angles of a triangle are in the ratio of 2:4:6. What is the measure of the smallest angle of the triangle?

Answer 1

\(\large \frac{2}{2+4+6} (180)\)

Answer 2

How'd you get that?

Answer 3

angle sum property gives u :
sum of angles = 180

Answer 4

since the angles are in ratio 2 : 4 : 6,
the smallest angle wud be 2/(2+4+6) th of the entire sum

Answer 5

if above doesnt make sense, try another method

Answer 6

say, the angles are : 2x, 4x and 6x

Answer 7

by angle sum property they must add up to 180 :

2x + 4x + 6x = 180

solve x

Answer 8

x = 15..

Answer 9

what does x represent?

Answer 10

x = 15,
so the smallest angle is 2x = 2*15 = 30

Answer 11

x is just the common factor

30 : 60 : 90

Answer 12

if u cancel out 15's, u wud get :

2 : 4 : 6

Answer 13

if u further cancel out 2's, u wud get :

1 : 2 :3

Answer 14

in ratios,

1 : 2 :3

is same as

2 : 4 : 6

is same as

3 : 12 : 18

...

Answer 15

you can think of the previous "x" as a scaling factor

Answer 16

okayy, thanks again.

Answer 17

u wlc!

Answer 18

wait so can you do x + 2x + 3x = 180?

Answer 19

as the same thing as 2:4:6

Answer 20

corrected a typo :

in ratios,

1 : 2 :3

is same as

2 : 4 : 6

is same as

\(\color{red}{6}\): 12 : 18

...

Answer 21

of course yes !

Answer 22

that gives u the same answer

Answer 23

x + 2x + 3x = 180

solve x

Answer 24

30

Answer 25

so, the smallest angle = x = 30

Answer 26

ohhhhh

Answer 27

okay that makes sense.

Answer 28

youre awesome :)

Answer 29

haha no you're awesome !

Answer 30

lol well thank you.