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.

of course there's an equation.

5/8 y + y + 1/4 y = 180
y = 96
so, x = 60 and z = 24

To solve this problem, let's first assign variables to the measures of the angles. Let's call the measure of angle Y, y.

According to the problem, angle X is 5/8 as large as angle Y. Therefore, we can represent the measure of angle X as (5/8)y.

Similarly, angle Z is 1/4 as large as angle Y. Therefore, we can represent the measure of angle Z as (1/4)y.

Now, we know that the sum of the measures of the angles in a triangle is always 180 degrees. So, we can write the equation:

(angle X) + (angle Y) + (angle Z) = 180

Substituting the values we obtained earlier, we get:

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

To simplify the equation, let's first convert the fractions to have the same denominator:

(10/16)y + (16/16)y + (4/16)y = 180

Now, let's add the fractions:

(30/16)y = 180

To isolate y, we can multiply both sides of the equation by the reciprocal of (30/16), which is (16/30) or (8/15):

(30/16)y * (16/30) = 180 * (8/15)

Simplifying, we get:

y = 96

Now, we can find the measures of angle X and angle Z using the values we obtained earlier:

Angle X = (5/8)y = (5/8) * 96 = 60
Angle Z = (1/4)y = (1/4) * 96 = 24

Therefore, the measures of all three angles in Triangle XYZ are:
Angle X = 60 degrees
Angle Y = 96 degrees
Angle Z = 24 degrees