In Triangle XYZ, the measure of angle X is 5/8 as large as the measure of angle Y. If the measure of angle Z is 1/4 as large as the measure of the angle Y, what's the measure of all three angles.

I've tried making up numbers to fit in the problem, but nothing is working. My teacher gave a hint that there is an equations that would figure this out.

see your previous post:

http://www.jiskha.com/display.cgi?id=1493340120

To solve this problem, let's start by assigning variables to the angles. Let's say that the measure of angle Y is represented by 'y'. Given that the measure of angle X is 5/8 as large as the measure of angle Y, we can write the equation:

X = (5/8)y

Similarly, the measure of angle Z is 1/4 as large as the measure of angle Y, so we can write another equation:

Z = (1/4)y

Now, since the sum of the angles in a triangle is always 180 degrees, we can write the equation:

X + Y + Z = 180

Now, substitute the expressions for X and Z from the previous equations into the third equation:

(5/8)y + y + (1/4)y = 180

Combine the terms:

(5/8 + 1 + 1/4)y = 180

To simplify, convert the fractions to the same denominator:

(5/8 + 8/8 + 2/8)y = 180

(15/8)y = 180

Multiply both sides by (8/15) to isolate 'y':

y = (180)(8/15)

y = 96

Now, substitute the value of 'y' back into the equations for X and Z to find their measures:

X = (5/8)(96) = 60

Z = (1/4)(96) = 24

So, the measure of angle X is 60 degrees, the measure of angle Y is 96 degrees, and the measure of angle Z is 24 degrees.