Question

the angle measure of three angles of triangle are p,q and r. angle measure of q is one-third of p and r is difference of p and q .find all angles

Answer 1

Step-by-step explanation:

In this question, i think we have to determine all the three angles of a triangle.

Since the three angles of a triangle are p,q and r.

Since, angle measure of q is one third of p, which implies

q=\frac{p}{3}q=

3

p

Angle measure of r is the difference of p and q, which implies

r=p-qr=p−q (Equation 1)

By using the angle sum property of a triangle which states that the sum of all the angles of a triangle is 180^{\circ}180

∘

p+q+r=180^{\circ}180

∘

Substituting the value of r from Equation 1,

p+q+p-q=180^{\circ}180

∘

2p=180^{\circ}180

∘

p=90^{\circ}90

∘

Since q=\frac{p}{3}q=

3

p

q=\frac{90}{3} = 30^{\circ}q=

3

90

=30

∘

Since, r=p-q

r =90^{\circ}-30^{\circ}=60^{\circ}90

∘

−30

∘

=60

∘