The angle measure of thre angle of a triangle are p, q and r. Angle measure of q is one third of p and r is the difference of p

The measures of the angles in the triangle are represented as p, q, and r.

Since the angles of a triangle add up to 180 degrees, we have:

p+q+r=180

Angle q is defined as one third of angle p, hence:

q=p

The angle r is determined by the difference between p and q:

r=p-q

Substituting for q gives:

So, r=p-q=p-

From this, we can derive:

r=

Then it follows:

r=

r=

Given that p+q+r=180, with q= and r=, we arrive at:

p++=180

To eliminate the fraction, let's multiply the complete expression by 3:

3*p+ 3*+ 3*=3*180

We simplify to find:

3p+p+2p=540

Thus, 6p=540

Dividing by 6 gives us:

So, p=90

With p=90, we find:

q=

q=

q=30

And for r, we calculate:

r=

r=

r=

Thus, we conclude p=90, q=30, r=60

The triangle's angle measures are 90, 30, and 60

In this problem, we need to find the measures of all three angles in a triangle.

Let the angles be represented as p, q, and r.

Given that the measure of angle q is one-third of angle p, we have:

The measure of angle r represents the difference between angles p and q, which gives us:

(Equation 1)

Applying the triangle angle sum property, it is known that the cumulative angle measure in a triangle is

p+q+r=

Substituting the value for r from Equation 1, we find:

p+q+p-q=

2p=

Thus, p=

Since

Since angle r is equal to p-q, we can conclude:

r =