In ∆PQR, if 3∠P = 4∠Q = 6∠R, calculate the angles of the triangle.
Solution:
Given, PQR is a triangle.
We have to find the angles of the triangle.
Given, 3∠P = 4∠Q = 6∠R
So, ∠P = (6/3)∠R
∠P = 2∠R
Also, ∠Q = (6/4)∠R
∠Q = (3/2)∠R
Angle sum property of a triangle states that the sum of all three interior angles of a triangle is always equal to 180 degrees.
∠P + ∠Q + ∠R = 180°
2∠R + (3/2)∠R + ∠R= 180°
∠R(2 + 3/2 + 1) = 180°
∠R(3 + 3/2) = 180°
∠R(9/2) = 180°
∠R = 180°(2/9)
∠R = 20°(2)
∠R = 40°
Now, ∠P = 2(40°) = 80°
∠Q = (3/2)(40°) = 2(20°) = 60°
Therefore, the angles are 80°, 60° and 40°.
✦ Try This:In ∆ABC, if 6∠A = 2∠B = 3∠C, calculate the angles of the triangle.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6
NCERT Exemplar Class 7 Maths Chapter 6 Problem 131
In ∆PQR, if 3∠P = 4∠Q = 6∠R, calculate the angles of the triangle.
Summary:
In ∆PQR, if 3∠P = 4∠Q = 6∠R, the angles of the triangle are 80°, 60° and 40°.
☛ Related Questions:
visual curriculum