Question

The second angle in a triangle is one third as the first. The third angle is two thirds as large as the first angle. Plz find the angle measures (plz show work). Thanks for your help.

Answer 1

So,

We know that the sum of the angles in a triangle will always equal 180°.

x + y + z = 180


`y= (1)/(3)x`


`z= (2)/(3) x`

We can substitute 1/3x for y and 2/3x for z in the first equation.


`x+ (1)/(3) x+ (2)/(3)x=180`

Collect Like Terms.
2x = 180

Divide both sides by 2.
x = 90

Substitute in the second equation.


`y= (1)/(3)(90)`

y = 30

Substitute in the third equation.


`z= (2)/(3) (90)`

z = 60

Let's check our values.

x = 90
y = 30
z = 60

x + y + z = 180?

90 + 30 + 60 = 180?

90 + 90 = 180?

180 = 180 YES!

This checks.

The first angle is 90°, the second angle is 30°, and the third angle is 60°.