Question

The smallest angle in a triangle measures 90* less than the largest angle . The middle angle measures 60* less than the largest . Find the measure of each angle

Answer 1

Okay let the smallest angle be x, middle angle be y and the largest one be z

Answer 2

ok

Answer 3

So:
x = z-90
y - z - 60

Answer 4

ok

Answer 5

...thinking...

Answer 6

now

Answer 7

Oh and finally:
x+y+z = 180

Answer 8

plug in ur x and y values

Answer 9

so is it 180-150?

Answer 10

x = z-90
y = z - 60
x+y+z=180
z-90 + z-60 + z = 180

Answer 11

3z - 150 = 180
3z = 180 + 150
3z = 330
z = 110

Answer 12

x = z - 90 = 110 - 90 = 20
y = z - 60 = 110 - 60 = 50

Answer 13

im so confused

Answer 14

how? tell me where u are confused.

Answer 15

well you wrote z=110 and then you put like 5 more steps. how long did it take you to learn this I seriously want to get this down.

Answer 16

Okay here look:
I said let x be the smallest, y be the middle, and z be the largest
smallest is 90 less than the largest, therefore:
x = z - 90
middle is 60 degrees less than the larges therefore:
y = z-60

Answer 17

Now sum of all angles in a triangle is given to be 180. That u have to know just memorize it.. sum is 180, so:
smallest + medium + largest = 180
x + y + z = 180
Plug in what you had for x and y, remember how we let:
x = z - 90, y = z - 60
(z - 90) + (z - 60) + z = 180

Answer 18

Simplify that a bit further:
z - 90 + z - 60 + z = 180
z + z + z - 60 - 90 = 180
3z - 150 = 180

Answer 19

3z - 150 + 150 = 180 + 150
3z + 0 = 180 + 150
3z = 330
Divide everything by 3:
z = 110

Answer 20

Now you know the largest angle: z = 110
Smallest is 90 less than largest: x = z - 90 = 110 - 90 = 20
Medium is 60 less than largest: y = z - 60 = 110 - 60 = 50