Home
Class 10
MATHS
The angles of a triangle are in AP. The ...

The angles of a triangle are in AP. The greatest angle is twice the least. Find all the angles of the triangle.

Text Solution

Verified by Experts

Let angles of the triangle be a-d, a, a+d.
`:. A-d+a+a+d=180^(@)`
`rArr 3a=180^(@) rArr a=60^(@)`
and `a+D=a(a-d)`
`rArr 60^(@)+d=2(60^(@)-d)`
`rArr 60^(@)+d=120^(@)-2d`
`rArr 3d=60^(@) rArr d=20^(@)`
`:. A-d=60^(@)-20^(@)=40^(@)`
`a+d=60^(@)+20^(@)=80^(@)`
`:.` Three angles of triangle are `40^(@),60^(@),80^(@)`.
Promotional Banner

Topper's Solved these Questions

  • ARITHMETIC PROGRESSION

    NAGEEN PRAKASHAN ENGLISH|Exercise Problem From NCERT/exemplar|20 Videos

  • ARITHMETIC PROGRESSION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 5a|5 Videos

  • AREA RELATED TO CIRCLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise Long Answer Question|5 Videos

  • CIRCLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Long Answer Questions|2 Videos

Similar Questions

Explore conceptually related problems

The angles of a triangle are in A.P. The greatest angle is twice the least. Find all the angles

The angles of a triangle are in A.P. If the greatest angle is double the least, find the angles.

The angles of a triangle are in A.P. If the greatest angle is double the least, then the ratio of the angles (in increasing order) is 2:3:4 (b) 1:2:3 (c) 3:4:5 (d) none of these

If the angles if a triangle are in A.P and tangent of the smallest angle is 1 then find all the angles of the triangle .

Find all the angles of an equilateral triangle.

In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle.

If the lengths of the sides of a triangle are in AP and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle is

If the lengths of the sides of a triangle are in AP and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle is

The angles of a triangle are in the ratio 3:4: 5. Find the smallest angle.

The angles of a triangle are in A.P. The ratio of the smallest angle in an grades and largest angle in radian is 40:pi . Find all angles of the triangle in degrees.