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
2 answers:
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 =
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